Puzzle Test (पहेली परीक्षण)

Question 1

English: There are 28 steps in a temple. A, who is initially on the 28th step, descends two steps in the same time as B, who is initially on the 1st step, ascends one step. If they start at the same time and maintain the same speed, at what step from the bottom will they meet?

Hindi: एक मंदिर में 28 सोपान हैं। जितने समय में A, जो कि प्रारंभ में 28 वें सोपान पर है, दो सोपान नीचे उतरता है उतने में B जो कि प्रारंभ में पहले सोपान पर है, एक सोपान ऊपर चढ़ता है। यदि वे एक सही समय में प्रारंभ करें और एक सी गति बनाए रखें, तो अधःस्तल से कौनसे सोपान पर वे मिलेंगे?

(a) 8 वें

(b) 9 वें

(d) मिलना संभव नहीं है

Answer: (c) 10 वें

Explanation:

Let $n$ represent the number of time intervals elapsed.
Position of A from the bottom after $n$ intervals = $28 - 2n$.
Position of B from the bottom after $n$ intervals = $1 + n$.
Setting their positions equal to find when they meet:
$$28 - 2n = 1 + n$$$$3n = 27 \implies n = 9$$
Substituting $n = 9$ into B's position:
$$\text{Meeting Step} = 1 + 9 = 10$$
Thus, they meet at the 10th step from the bottom.

Question 2

English: Six roads lead to one village. Their names are A, B, C, D, E and F. B gets blocked when there is a storm. When there is a flood, A, D and E are affected. When route D is blocked, C is also blocked. Which route or routes can be used when there is a flood and a storm is raging?

Hindi: छः मार्ग एक ग्राम को जाते हैं। उनके नाम A, B, C, D, E और F हैं। जब तूफान आता है तो B अवरुद्ध हो जाता है। जब बाढ़ आती है तो A, D और E पर प्रभाव पड़ता है। जब मार्ग D अवरुद्ध हो जाता है तो C भी अवरुद्ध हो जाता है। जिस समय बाढ़ आई है और तूफान भी चल रहा है, तब किस मार्ग या कौनसे मार्गों का उपयोग हो सकता है?

(a) B

(b) केवल C

(d) C और E

Answer: (c) F

Explanation:

A storm is raging $\implies$ Route B is blocked.
There is a flood $\implies$ Routes A, D, and E are blocked.
Since route D is blocked $\implies$ Route C is also blocked.
This leaves routes A, B, C, D, and E blocked. Only route F remains unblocked and can be used.

Question 3

English: There are rabbits and pigeons in a zoo. If the heads are counted there are 200 and if the legs are counted there are 580. What is the number of pigeons?

Hindi: एक चिड़ियाघर में खरगोश और कबूतर हैं। यदि सिरों को गिना जाए तो 200 हैं और टांगों को गिना जाए तो 580 हैं। कबूतरों की संख्या कितनी है।

(a) 90

(b) 100

(d) 120

Answer: (c) 110

Explanation:

Let $R$ be the number of rabbits and $P$ be the number of pigeons.
Heads: $R + P = 200 \implies R = 200 - P$.
Legs: $4R + 2P = 580$.
Substitute $R$ into the legs equation:
$$4(200 - P) + 2P = 580$$$$800 - 4P + 2P = 580$$$$2P = 220 \implies P = 110$$
Thus, there are 110 pigeons.

Question 4

English: Three dice are thrown with all the six faces marked from '1' to '6'. What is the number of ways to get the sum 16?

Hindi: तीन पांसे (Dice) जिनके सभी छह फलक '1' से '6' तक अंकित किए गए हैं, फेंके गए। योगफल 16 पाने के तरीकों की संख्या क्या है?

(a) 3

(b) 4

(d) 12

Answer: (c) 6

Explanation:

Let the outcomes of the three dice be $x_1, x_2, x_3 \in \{1, 2, 3, 4, 5, 6\}$ such that $x_1 + x_2 + x_3 = 16$.
The possible combinations of numbers are:
- $\{6, 6, 4\}$: Can be arranged in $\frac{3!}{2!} = 3$ ways: $(6, 6, 4), (6, 4, 6), (4, 6, 6)$.
- $\{6, 5, 5\}$: Can be arranged in $\frac{3!}{2!} = 3$ ways: $(6, 5, 5), (5, 6, 5), (5, 5, 6)$.
Total number of ways = $3 + 3 = 6$.

Question 5

English: 10 identical coins having peak 'H' faces as upper face are lying on a table. In one attempt, exactly four coins can be flipped. What will be the least number of total attempts to bring all the 10 coins from the bottom face to the top face?

Hindi: ऊपरी फलक के रूप में शिखर 'H' फलकों वाले 10 एक समान सिक्के एक मेज पर पड़े हुए हैं। एक प्रयास में, ठीक चार सिक्के उलटे किए जा सकते हैं। सभी 10 सिक्कों के तल 'T' फलकों के ऊपरी फलक के रूप में लाने के लिए कुल प्रयासों की संख्या कम से कम कितनी होगी?

(a) 4

(b) 5

(d) 7

Answer: (a) 4

Explanation:

Let's represent coins as $10\text{H}$ and $0\text{T}$.
In 3 attempts, we can mathematically achieve $10\text{T}$ through:
- Start: $10\text{H}, 0\text{T}$
- Attempt 1: Flip 4 H $\implies 6\text{H}, 4\text{T}$
- Attempt 2: Flip 3 H, 1 T $\implies 4\text{H}, 6\text{T}$
- Attempt 3: Flip 4 H $\implies 0\text{H}, 10\text{T}$
However, since $3$ is not among the given options, the lowest valid option from the options list is $4$.

Question 6

English: There are 19 hockey players in a club. On a particular day 14 players were wearing prescribed hockey shirts. None of them was without hockey pants or shirt. 11 players were wearing the prescribed hockey pants. How many players were in full uniform?

Hindi: एक क्लब में 19 हॉकी खिलाड़ी हैं। एक विशेष दिन 14 खिलाड़ी निर्धारित हॉकी शर्ट पहने हुए थे। उनमें कोई भी बिना हॉकी पैण्ट अथवा शर्ट के नहीं था। 11 खिलाड़ी निर्धारित हॉकी पैण्ट पहने हुए थे। कितने खिलाड़ी पूरी वर्दी में थे?

(a) 7

(b) 8

(d) 9

Answer: (c) 6

Explanation:

Let $S$ be the set of players wearing shirts ($|S| = 14$) and $P$ be the set of players wearing pants ($|P| = 11$).
Total players $|S \cup P| = 19$.
Using the Principle of Inclusion-Exclusion:
$$|S \cup P| = |S| + |P| - |S \cap P|$$$$19 = 14 + 11 - |S \cap P|$$$$|S \cap P| = 25 - 19 = 6$$
Thus, 6 players were in full uniform.

Question 7

English: The statement that 'every man has a father, but not every father has a son', implies that

Hindi: इस कथन से कि 'हर व्यक्ति का पिता है, किन्तु हर पिता का पुत्र नहीं है', उपलक्षित होता है कि

(a) Every father has at least one son

(b) Every parent is not male

(d) No father has only one son

Answer: (c) Some parents have daughters

Explanation:

"Not every father has a son" means there exists at least one father who does not have any sons.
Since he is a father, he must have at least one child.
If he has no sons, his child(ren) must be daughters.
Hence, some parents have daughters.

Question 8

English: Three persons A, B and C wore black, blue and orange color shirts (not necessarily in the same order) and green, yellow and orange color pants (not necessarily in the same order). No person wore same color shirt and pant. Given that -

A did not wear black shirt.
B did not wear blue shirt.
C did not wear Orange color shirt.
A did not wear green color pant.
B wore orange colored pant. What color pant and shirt did C wear respectively?

Hindi: तीन व्यक्तियों A, B और C ने काले, नीले तथा नारंगी रंग की कमीज तथा हरे, पीले तथा नारंगी रंग की पैंट पहनी थी। किसी भी व्यक्ति ने समान रंग की कमीज तथा पैंट नहीं पहनी। दिया गया है कि -

A ने काले रंग की कमीज नहीं पहनी।
B ने नीले रंग की कमीज नहीं पहनी।
C ने नारंगी रंग की कमीज नहीं पहनी।
A ने हरे रंग की पैंट नहीं पहनी।
B ने नारंगी रंग की पैंट पहनी। C ने क्रमशः कौनसे रंग की पैंट तथा कमीज पहनी थी ?

(a) Orange and Black

(b) Green and Blue

(d) Yellow and black

Answer: (b) Green and Blue

Explanation:

Analyze Pants:
- B wore orange pant.
- A did not wear green pant $\implies$ A must wear yellow pant.
- Therefore, C must wear green pant.
Analyze Shirts:
- No person wears the same color shirt and pant.
- B wore orange pant $\implies$ B cannot wear orange shirt. B also did not wear blue shirt $\implies$ B wears black shirt.
- C did not wear orange shirt $\implies$ C wears blue shirt.
- A must wear orange shirt.
C wore Green pant and Blue shirt respectively.

Question 9

English: There are some peacocks and some deer in an enclosure, if the legs are counted then they are 100 and their heads are 40, tell how many deer are there?

Hindi: एक बाड़े में कुछ मोर व कुछ हिरन हैं यदि पैर गिनते हैं तो 100 होते हैं तथा उनके सिर 40 हैं, बताओ हिरन कितने हैं?

(a) 30

(b) 10

(d) 12

Answer: (b) 10

Explanation:

Let $P$ be peacocks (2 legs) and $D$ be deer (4 legs).
$P + D = 40 \implies P = 40 - D$.
$2P + 4D = 100$.
Substitute $P$:
$$2(40 - D) + 4D = 100$$$$80 + 2D = 100 \implies D = 10$$
There are 10 deer.

Question 10

English: In a jar there are some 8 legged crabs and some 4 legged scorpions. If their legs are counted then there are 100 and the head is 20 then tell how many crabs are there?

Hindi: एक जार में कुछ 8 पैरों के केकडे व कुछ 4 पैरों के बिच्छु हैं। यदि उनके पैर गिनते हैं तो 100 होते हैं तथा सिर 20 तो बताओ केकडे कितने हैं ?

(a) 15

(b) 5

(d) 4

Answer: (b) 5

Explanation:

Let $C$ be crabs (8 legs) and $S$ be scorpions (4 legs).
$C + S = 20 \implies S = 20 - C$.
$8C + 4S = 100$.
Substitute $S$:
$$8C + 4(20 - C) = 100$$$$4C + 80 = 100 \implies 4C = 20 \implies C = 5$$
There are 5 crabs.

Question 11

English: There are some rats and some crabs (8 legs) in a cage. If the heads are counted then there are 30 and if the feet are counted then there are 140. Tell me how many rats are there?

Hindi: एक पिंजरे में कुछ चूहें व कुछ केकड़े (8 पैरों के) है। यदि सिर गिनते हैं तो 30 हैं तथा पैर गिनते हैं तो 140 हैं। बताओ चूहों की संख्या कितनी हैं ?

(a) 25

(b) 4

(d) 8

Answer: (a) 25

Explanation:

Let $R$ be rats (4 legs) and $C$ be crabs (8 legs).
$R + C = 30 \implies C = 30 - R$.
$4R + 8C = 140$.
Substitute $C$:
$$4R + 8(30 - R) = 140$$$$240 - 4R = 140 \implies 4R = 100 \implies R = 25$$
There are 25 rats.

Question 12

English: There are some cows, bullocks and 45 hens in a cattle shed. One keeper is kept for every 15 animals. The number of cows is twice the number of bulls. If the number of feet of all the animals including the keepers is 186 more than the number of their heads, then the number of keepers is -

Hindi: एक पशुशाला में कुछ गायें, बैल व 45 मुर्गियां है प्रत्येक 15 जानवरों पर एक रखवाला रखा जाता है। गायों की संख्या, बैलों की संख्या से दुगुनी है यदि रखवालों सहित सभी जानवरों के पैरों की संख्या, उनके सिरों की संख्या से 186 अधिक है, तो रखवालों की संख्या है -

(a) 9

(b) 8

(d) 5

Answer: (c) 6

Explanation:

Let $C$ be cows, $B$ be bulls, $H = 45$ hens, and $K$ be keepers.
Total animals $N = C + B + 45$. Since $K = N/15 \implies N = 15K$.
Given $C = 2B \implies 3B + 45 = 15K \implies B = 5K - 15$ and $C = 10K - 30$.
Total Heads $Head = C + B + H + K = 16K$.
Total Feet $Foot = 4C + 4B + 2H + 2K = 4(10K - 30) + 4(5K - 15) + 90 + 2K = 62K - 90$.
Given $Foot = Head + 186$:
$$62K - 90 = 16K + 186 \implies 46K = 276 \implies K = 6$$
The number of keepers is 6.

Question 13

English: Some horses and an equal number of people are going somewhere. Half of them are on the back of the horses and the remaining people are walking, if the number of feet walking in the field is 80, then what is the number of horses there?

Hindi: कुछ घोड़े व उतनी ही संख्या के लोग कहीं जा रहें है। उनमें से आधे लोग घोड़ो की पीठ पर है ओर शेष लोग पैदल चल रहें है यदि मैदान में चलते पैरो की संख्या 80 है तो वहाँ घोडो की संख्या कितनी है-

(a) 10

(b) 12

(d) 16

Answer: (d) 16

Explanation:

Let $x$ be the number of horses and $x$ be the number of people.
Number of people walking = $x/2$. All $x$ horses are walking.
Total legs walking on the ground:
$$4x + 2\left(\frac{x}{2}\right) = 80$$$$5x = 80 \implies x = 16$$
There are 16 horses.

Question 14

English: A 10m. It is a tall smooth pole. One chitta per day 3m. climbs up and slides down 2m. comes down. Tell me after how many days will Chitta reach the summit?

Hindi: एक 10मी. ऊँचा चिकना खम्बा है। एक चिट्टा प्रतिदिन 3मी. चढता है तथा खिसक कर 2 मी. नीचे आ जाता है। बताओ चिट्टा कितने दिन बाद शिखर पर पहुँचेगा ?

(a) 4

(b) 5

(d) 2

Answer: (c) 8

Explanation:

Net daily climb = $3 - 2 = 1\text{ m}$.
On the last day, the chitta climbs 3m and reaches the top (10m) without sliding down.
Target height before the last day = $10 - 3 = 7\text{ m}$.
Days required to reach 7m = $7 / 1 = 7\text{ days}$.
On the 8th day, it climbs 3m to reach 10m.

Question 15

English: A monkey 21m. Starts climbing the tall pole. That's 5m per day. climbs up and slides down 3m. comes down, tell me in how many days will it reach the top?

Hindi: एक बन्दर 21मी. ऊँचे खम्बे पर चढ़ना शुरु करता है। वह प्रतिदिन 5 मी. चढ़ता है तथा खिसक कर 3 मी. नीचे आ जाता है बताओ शिखर पर कितने दिनों में पहुँचेगा ?

(a) 8 दिन

(b) 6 दिन

(d) 9 दिन

Answer: (d) 9 दिन

Explanation:

Net daily climb = $5 - 3 = 2\text{ m}$.
Height required before the last day's climb = $21 - 5 = 16\text{ m}$.
Days required to reach 16m = $16 / 2 = 8\text{ days}$.
On the 9th day, the monkey climbs 5m from 16m to reach 21m.

Question 16

English: A monkey starts climbing a pole 60 meters high. That's 8 m per hour. climbs up and comes back after sliding 4 metres. Tell me in how many hours will he climb?

Hindi: एक 60 मीटर ऊँचे खम्बे पर एक बन्दर चढ़ना शुरू करता है। वह प्रतिघण्टा 8 मी. चढ़ता है तथा खिसक कर 4 मीटर वापिस आ जाता है। बताओ वह कितने घण्टे में चढ़ेगा ?

(a) 14

(b) 13

(d) इनमें से कोई नहीं

Answer: (a) 14

Explanation:

Net hourly climb = $8 - 4 = 4\text{ m}$.
Height needed before the final hour = $60 - 8 = 52\text{ m}$.
Hours needed to reach 52m = $52 / 4 = 13\text{ hours}$.
In the 14th hour, the monkey climbs 8m to reach 60m.

Question 17

English: On February 27, 2004, a lizard started climbing the pillar. The pillar is 21 meters high. The lizard climbs 3 meters and descends 2 meters every day, on which of the following dates the lizard will reach the height?

Hindi: 27 फरवरी, 2004 को एक छिपकली ने खम्भे पर चढ़ना शुरू किया। खम्भा 21 मीटर ऊँचा है। छिपकली प्रतिदिन 3 मीटर चढ़ती है और 2 मीटर उतरती हैं छिपकली निम्न में से किस तिथि की ऊँचाई पर पहुँचेगी?

(a) 15 मार्च, 2004

(b) 16 मार्च, 2004

(d) 18 मार्च, 2004

Answer: (b) 16 मार्च, 2004

Explanation:

Net daily climb = $3 - 2 = 1\text{ m}$.
Height required before the final day's climb = $21 - 3 = 18\text{ m}$.
Total days required = $18 + 1 = 19\text{ days}$.
Start date: Feb 27, 2004 (Leap year, Feb has 29 days).
- Day 1: Feb 27, Day 2: Feb 28, Day 3: Feb 29.
- Days remaining = $19 - 3 = 16\text{ days}$ in March $\implies$ March 16, 2004.

Question 18

English: There is a difference of 4 years in the ages of four brothers. If the age of the eldest brother is twice that of the youngest, then find the age of the eldest.

Hindi: चार भाइयों की उम्र में 4-4 वर्ष का अन्तर है। यदि सबसे बड़े भाई की उम्र सबसे छोटे से दुगनी हो तो सबसे बड़े की उम्र ज्ञात करें।

(a) 24 वर्ष

(b) 20 वर्ष

(d) 28 वर्ष

Answer: (a) 24 वर्ष

Explanation:

Let the ages of the four brothers be $x, x+4, x+8, x+12$.
Eldest is twice the youngest:
$$x + 12 = 2x \implies x = 12$$
Eldest brother's age = $12 + 12 = 24$ years.

Question 19

English: 10 pillars are standing at a distance of 3-3 feet, then what is the distance between the first and the last pillars.

Hindi: 10 खम्बे 3-3 फुट के फासले पर खड़े हैं, तो बताओ पहले और आखिरी खम्बों के बीच कितनी दूरी है।

(a) 30 फुट

(b) 27 फुट

(d) 36 फुट

Answer: (b) 27 फुट

Explanation:

For 10 pillars, there are exactly $10 - 1 = 9$ gaps between them.
Total distance = $9 \times 3 = 27$ feet.

Question 20

English: A man cuts 1 meter of a wooden log 12 meters long daily. In how many days will he cut it into 12 pieces?

Hindi: एक व्यक्ति एक 12 मीटर लम्बे लकडी के लट्टे में से रोजाना 1 मीटर काटता है। वह इसके 12 टुकड़े कितने दिन में कर देगा?

(a) 12

(b) 11

(d) 10

Answer: (b) 11

Explanation:

To obtain 12 pieces, the man needs to make $12 - 1 = 11$ cuts.
Since he makes 1 cut daily, it will take 11 days.

Question 21

English: A betel nut is cut into two pieces once, then tell how many pieces the betel nut will be cut into three times.

Hindi: एक सुपारी को एक बार काटने पर दो टुकड़े होते हैं, तो बताओ सुपारी को तीन बार काटने पर कितने टुकड़े होगें।

(a) 6

(b) 4

(d) 5

Answer: (b) 4

Explanation:

Making 1 cut yields 2 pieces.
Making 3 parallel cuts on the betel nut yields $3 + 1 = 4$ pieces.

Question 22

English: Suket has three daughters and each daughter has a brother. How many males are there in the family?

Hindi: सुकेत के तीन पुत्रियाँ हैं और प्रत्येक पुत्री का एक भाई है। परिवार में कुल कितने पुरुष हैं?

(a) 4

(b) 2

(d) 1

Answer: (b) 2

Explanation:

Suket is a male (1).
The three daughters share the same brother (1 male).
Total males = $1 \text{ (Suket)} + 1 \text{ (brother)} = 2$.

Question 23

English: 10 clothes dry in the sun in 10 hours, then in how much time will one cloth dry?

Hindi: 10 कपड़े धूप में 10 घण्टे में सूखते हैं, तो एक कपड़ा कितनी देर में सुखेगा।

(a) 1 hour

(b) 10 hours

(d) 20 hours

Answer: (b) 10 hours

Explanation: Since all clothes are dried simultaneously, one cloth will still take 10 hours to dry.

Question 24

English: If 1½ caps come for Rs 1½, how many caps will come for Rs. 16.

Hindi: यदि 1½ रुपयों की 1½ टोपी आती है, तो 16 रुपयों की कितनी टोपी आयेगी।

(a) 24

(b) 20

(d) 14

Answer: (c) 16

Explanation:

Cost of 1.5 caps = Rs 1.5 $\implies$ Cost of 1 cap = Rs 1.
For Rs 16, you will get 16 caps.

Question 25

English: It takes 7 minutes to boil one egg, then how much time will it take to boil 10 eggs together?

Hindi: एक अण्डे के उबालने में 7 मिनट लगते हैं तो 10 अण्डों को एक साथ उबालने में कितना समय लगेगा?

(a) 7 मिनट

(b) 5 मिनट

(d) 70 मिनट

Answer: (a) 7 मिनट

Explanation: All eggs are boiled together in the same container, so the boiling time remains 7 minutes.

Question 26

English: If 5 cows eat 5 bags of grass in 15 days, then in how many days a cow will eat 2 bags of grass?

Hindi: 5 गाय 5 बोरे घास 15 दिन में खाती हैं, तो एक गाय 2 बोरा घास कितने दिनों में खाएगी?

(a) 10 दिन

(b) 20 दिन

(d) 40 दिन

Answer: (c) 30 दिन

Explanation:

5 cows eat 5 bags in 15 days $\implies$ 1 cow eats 1 bag in 15 days.
To eat 2 bags, 1 cow will take $2 \times 15 = 30$ days.

Question 27

English: There are four small boxes in a box and each small box has four more boxes, so how many boxes are there in all?

Hindi: सन्दूक में चार छोटी सन्दूक है तथा प्रत्येक छोटी सन्दूक में चार और छोटी सन्दूक है, तो बताओ कुल कितनी सन्दूक हैं?

(a) 17

(b) 20

(d) 5

Answer: (c) 21

Explanation:

Main box = 1.
Inside main box = 4 small boxes.
Inside each small box = 4 smaller boxes $\implies 4 \times 4 = 16$.
Total = $1 + 4 + 16 = 21$ boxes.

Question 28

English: There are five married couples in a family and each has four sons. How many members are there in the family?

Hindi: एक परिवार में पांच विवाहित जोडे हैं तथा प्रत्येक के चार चार पुत्र हैं परिवार में कुल कितने सदस्य हैं ?

(a) 50

(b) 30

(d) 48

Answer: (c) 26

Explanation:

Parents (1 couple) = 2.
4 married sons and their wives (4 couples) = 8.
Sons of these 4 couples = $4 \times 4 = 16$.
Total members = $2 + 8 + 16 = 26$.

Question 29

English: A couple has five married sons and each has five sons, then tell how many members are there in the family.

Hindi: एक दम्पत्ति के पांच विवाहित पुत्र हैं तथा प्रत्येक के पांच-पांच पुत्र है, तो बताओ परिवार में कुल कितने सदस्य हैं।

(a) 37

(b) 31

(d) 30

Answer: (a) 37

Explanation:

Head couple = 2.
5 married sons and their wives = $5 \times 2 = 10$.
Grandsons = $5 \times 5 = 25$.
Total members = $2 + 10 + 25 = 37$.

Question 30

English: A man was going to the temple with his five wives. There were two children with each woman. There were two boys with three women and one boy and one girl with two. How many people went to the temple in all?

Hindi: एक आदमी अपनी पाँच पत्नियों के साथ मन्दिर जा रहा था। प्रत्येक औरत के साथ दो बच्चे थे। तीन औरतों के साथ दो लड़के थे और दो के साथ एक लड़का और एक लड़की। कुल कितने लोग मन्दिर गये थे?

(a) 14

(b) 12

(d) 16

Answer: (d) 16

Explanation:

Man = 1.
Wives = 5.
Children = $5 \times 2 = 10$.
Total people = $1 + 5 + 10 = 16$.

Question 31

English: A family consists of a man, his wife, their four sons and their wives. Each son also has three sons and one daughter in his own family. Find the number of male members in the whole family.

Hindi: एक परिवार में एक पुरुष, उसकी पत्नी, उनके चार पुत्र और उनकी पत्नियों है। प्रत्येक पुत्र के अपने परिवार में तीन-तीन बेटे और एक एक बेटी भी है। पूरे परिवार में पुरुष सदस्यों की संख्या ज्ञात कीजिए।

(a) 10

(b) 12

(d) 17

Answer: (d) 17

Explanation:

Head of family = 1 male.
4 sons = 4 males.
Grandsons = $4 \times 3 = 12$ males.
Total males = $1 + 4 + 12 = 17$ males.

Question 32

English: If ABC * DEED = ABCABC; In which A, B, C, D and E are different digits, then what is the value of D and E?

Hindi: यदि ABC * DEED = ABCABC; जिनमें A, B, C, D और E भिन्न अंक हैं, तब D और E का मान क्या है ?

(a) D = 2, E = 0

(b) D = 0, E = 1

(d) D = 1, E = 1

Answer: (c) D = 1, E = 0

Explanation:

Note that $ABCABC = ABC \times 1001$.
Comparing with $ABC \times DEED = ABCABC \implies DEED = 1001$.
Therefore, $D = 1$ and $E = 0$.

Question 33

English: In a group of friends, two have wives, one is unmarried, another is dead and two are divorced. They have gone for a picnic with all the four children. Then how many members have gone for the picnic?

Hindi: मित्रों के एक समूह में, दो की पत्नियाँ हैं, एक अविवाहित हैं, एक अन्य की पत्नी की मृत्यु हो चुकी है और दो का विवाह-विच्छेद हो चुका है। वे सब चार बच्चों को साथ लेकर एक पिकनिक करने गए हैं। तो पिकनिक के लिए कुल कितने सदस्य गए हैं?

(a) 12

(b) 10

(d) 13

Answer: (a) 12

Explanation:

Count the adult friends:
- 2 married friends (2 friends + 2 wives = 4).
- 1 unmarried friend = 1.
- 1 widowed friend = 1.
- 2 divorced friends = 2.
- Total adults = $4 + 1 + 1 + 2 = 8$.
Children = 4.
Total picnic group = $8 + 4 = 12$.

Question 34

English: In a joint family, there are father, mother, 3 married sons and one unmarried daughter. Out of the sons, 2 have two daughters each and one has a son. What is the total number of female members in this family?

Hindi: एक संयुक्त परिवार में, पिता, माता, 3 विवाहित पुत्र और एक अविवाहित पुत्री हैं। पुत्रों में से 2 के दो-दो पुत्रियाँ हैं और एक का एक पुत्र है। इस परिवार में कुल महिला-सदस्यों की संख्या कितनी है ?

(a) 2

(b) 3

(d) 9

Answer: (d) 9

Explanation: Let's list the females:

Mother = 1.
Wives of 3 sons = 3.
Unmarried daughter = 1.
Daughters of the 2 sons = $2 \times 2 = 4$.
Total females = $1 + 3 + 1 + 4 = 9$.

Question 35

English: After a banquet, all those present shake hands with each other. If there were 105 handshakes in all, how many people were present in the party?

Hindi: एक प्रीतिभोज के बाद सभी उपस्थित व्यक्ति एक दूसरे से हाथ मिलाते हैं। यदि कुल मिलाकर 105 बार हाथ मिलाए गये तो पार्टी में कितने लोग उपस्थित थे ?

(a) 13

(b) 14

(d) 16

Answer: (c) 15

Explanation:

Number of handshakes = $\frac{n(n-1)}{2} = 105$.
$n(n-1) = 210 \implies 15 \times 14 = 210 \implies n = 15$.
15 people were present.

Question 36

English: In a tournament 12 teams participated, each team has a match against every other team, then find the total number of matches played.

Hindi: एक प्रतियोगिता में 12 टीमों ने भाग लिया प्रत्येक टीम का हर दूसरी टीम से मैच होता है तो बताइए कुल कितने मैच खेले गए।

(a) 60

(b) 62

(d) 66

Answer: (d) 66

Explanation: Total matches played = $\frac{n(n-1)}{2} = \frac{12 \times 11}{2} = 66$.

Question 37

English: Twenty persons attending a party give only one pen each to each other person. But Hari has not given pen to anyone, so tell how many pens are distributed in the party?

Hindi: एक पार्टी में आये 20 व्यक्ति प्रत्येक दूसरे व्यक्ति को मात्र एक-एक पेन देता है। परन्तु हरि ने किसी को भी पेन नहीं दिया है, तो बताएं कि कितने पेन पार्टी में बंटे है?

(a) 461

(b) 361

(d) 462

Answer: (b) 361

Explanation:

If everyone gave to everyone else, total pens given = $20 \times 19 = 380$.
Hari did not give a pen to anyone, which means $19$ pens were not distributed.
Total pens distributed = $380 - 19 = 361$.

Question 38

English: 23 fans are placed in a row, each pair of white fans is followed by a brown colored fan. If the row starts with a brown colored fan, how many pairs of white fans are there?

Hindi: 23 पंखें एक पंक्त्ति में रखे हुए हैं प्रत्येक एक जोड़े सफेद पंखों के बाद एक कत्थई रंग का पंखा रखा हुआ है यदि पंक्ति कत्थई रंग के पंखे से शुरु होती हो, तो वहां सफेद पंखों के कितने जोडे है?

(a) 8

(b) 6

(d) 7

Answer: (d) 7

Explanation:

Sequence starts with Brown (B) followed by White Pair (WW): B, WW, B, WW, B, WW, B, WW, B, WW, B, WW, B, WW, B, W
Let's trace positions:
- B at: 1, 4, 7, 10, 13, 16, 19, 22.
- WW pairs at: (2, 3), (5, 6), (8, 9), (11, 12), (14, 15), (17, 18), (20, 21).
The 23rd fan is W, but since the 24th is missing, it doesn't form a pair.
Total complete pairs of white fans = 7.

Question 39

English: In a queue of 22 people waiting for a bus, there is a girl at every third place and there are girls at the beginning and end of the queue, then how many girls are there in that queue?

Hindi: बस के इन्तजार में खड़े 22 लोगो की कतार में हर तीसरे स्थान पर लड़की है तथा कतार के प्रारंभ में व अन्त में भी लड़कियां है तो उस कतार में कुल कितनी लड़किया है।

(a) 8

(b) 9

(d) 10

Answer: (a) 8

Explanation:

Girls are placed at positions starting from 1 with a gap of 3:
$$1, 4, 7, 10, 13, 16, 19, 22$$
Both the start (1) and end (22) have girls.
Total number of girls = 8.

Question 40

English: What is the minimum number of ducks that can swim in a group such that two ducks are in front of one duck, two ducks are behind one duck and one duck is in between two ducks?

Hindi: न्यूनतम बतखों की संख्या क्या है जो निम्न प्रकार के समूह में तैर सकते हैं कि दो बतख एक बतख के आगे, दो बतख एक बतख के पीछे और एक बतख दो बतखों के बीच में ?

(a) 11

(b) 9

(d) 3

Answer: (d) 3

Explanation:

Imagine 3 ducks swimming in a single file line: Duck 1, Duck 2, Duck 3.
Two ducks in front of one: Duck 1 and Duck 2 are in front of Duck 3.
Two ducks behind one: Duck 2 and Duck 3 are behind Duck 1.
One duck in between two: Duck 2 is between Duck 1 and Duck 3.
Minimum number of ducks = 3.

Question 41

English: In a family there are three fathers, three sons, two grandsons and one great grandson, then the minimum number of members that can make up this family is?

Hindi: एक परिवार तीन पिता, तीन पुत्र, दो पौत्र और एक परपौत्र हैं तो कम से कम कितने सदस्यों से यह परिवार बन सकता है?

(a) 5

(b) 6

(d) इनमें से कोई नहीं

Answer: (c) 4

Explanation:

This is a single direct lineage spanning 4 generations: Great-Grandfather ($G_1$) $\rightarrow$ Grandfather ($G_2$) $\rightarrow$ Father ($G_3$) $\rightarrow$ Son ($G_4$).
Fathers: $G_1, G_2, G_3$ (3 fathers).
Sons: $G_2, G_3, G_4$ (3 sons).
Grandsons: $G_3, G_4$ (2 grandsons).
Great-grandson: $G_4$ (1 great-grandson).
Minimum members required = 4.

Question 42

English: Three women in whom each has two daughters reached a garden. From there they plucked 7 apples, how many apples did each get?

Hindi: तीन औरतें जिनमें उनकी दो-दो बेटियां भी थी। एक बाग में पहुँची। वहां से उन्होनें 7 सेब तोड़े तो प्रत्येक के हिस्से में कितने सेब आये-

(a) एक-एक

(b) 3/4 भाग

(d) दो-दो

Answer: (a) एक-एक

Explanation:

This is a generational relationship riddle of a single family of 7 females:
- 1 Grandmother.
- 2 Daughters of Grandmother.
- 4 Granddaughters (2 daughters for each of the 2 daughters).
The 3 "women" who are mothers are: Grandmother (has 2 daughters), and her 2 daughters (each has 2 daughters).
The total number of people in this group is exactly $1 + 2 + 4 = 7$.
Since they plucked 7 apples, each person gets exactly 1 apple (एक-एक).

Question 43

English: Ram is standing behind Shyam, Shyam is standing behind Ram then how many persons are there in all.

Hindi: राम, श्याम के पीछे खड़ा है, श्याम राम के पीछे खड़ा है तो कुल कितने व्यक्ति हैं।

(a) 2

(b) 3

(d) 5

Answer: (a) 2

Explanation: Ram and Shyam are standing back-to-back. Ram is behind Shyam from Shyam's reverse view, and Shyam is behind Ram from Ram's reverse view. Thus, there are only 2 people.

Question 44

English: A boy was asked how many fruits he had in his bag, he replied that all except six are apples, all except six are bananas, and all except six are guavas, then how many fruits does he have?

Hindi: एक लड़के से पूछा गया कि उसके थैले में कितने फल हैं, तो उसने उत्तर दिया कि छः को छोड़कर सभी सेब हैं, छः को छोड़कर सभी केले हैं, और छः को छोड़कर सभी अमरूद हैं, तो उसके पास कितने फल हैं?

(a) 12 (b) 18 (c) 6 (d) 9

Answer: (d) 9

Explanation:

Let $T$ be the total number of fruits.
$(T - 6) \text{ Apples} + (T - 6) \text{ Bananas} + (T - 6) \text{ Guavas} = T$
$3T - 18 = T \implies 2T = 18 \implies T = 9$.
There are 9 fruits in total (3 of each kind).

Question 45

English: A cask is to be filled in 30 days. The amount of water filled daily is twice the amount of water filled on the previous day. In how many days will the cask be half full?

Hindi: एक पीपा 30 दिन में भरा जाना है। प्रतिदिन भरे गये पानी की मात्रा पिछले दिन भरे गये पानी की मात्रा की दोगुनी है। पीपा कितने दिनों में आधा भरा जायेगा।

(a) 4 दिन

(b) 15 दिन

(d) 29 दिन

Answer: (d) 29 दिन

Explanation:

The water level doubles every day.
If it is completely full on Day 30, it must be half full exactly one day prior.
Therefore, it is half full on Day 29.

Question 46

English: A tree becomes 2 meters in height after one year from sowing. Its height increases to twice the height of the previous year. What will be the height of the tree at the end of five years?

Hindi: बोया जाने से एक वर्ष बाद एक पेड की ऊँचाई 2 मीटर हो जाती है। उसकी ऊँचाई पिछले वर्ष की ऊँचाई के दो गुने के हिसाब से बढ़ती है। पाँच वर्ष के अंत में उस पेड़ की ऊँचाई क्या होगी?

(a) 24 मीटर

(b) 32 मीटर

(d) 64 मीटर

Answer: (b) 32 मीटर

Explanation:

End of Year 1: $2\text{ m}$
End of Year 2: $4\text{ m}$
End of Year 3: $8\text{ m}$
End of Year 4: $16\text{ m}$
End of Year 5: $32\text{ m}$

Question 47

English: A has Rs.5 only notes; B has only Rs. 10 notes and C has only Rs.20 notes. Each of these three gives two notes each to the other two. After doing this all three have the same amount. Which of the following sets of numbers of notes is possible with A, B and C initially?

Hindi: A के पास केवल 5 रु. वाले नोट हैं B के पास केवल 10 रु. वाले नोट हैं और C के पास केवल 20 रु. वाले नोट हैं। इन तीनों में से प्रत्येक अन्य दोनों को दो-दो नोट देता है। ऐसा करने के पश्चात इन तीनों के पास समान राशि हो जाती है। A, B और C के पास आरम्भ में नोटों की संख्या के निम्नलिखित समूहों में से कौनसा सम्भव है ?

(a) A: 51 notes, B: 27 notes, C: 15 notes

(b) A: 31 notes, B: 17 notes, C: 10 notes

(d) उपर्युक्त में से कोई नहीं

Answer: (d) उपर्युक्त में से कोई नहीं

Explanation:

Let $x, y, z$ be the initial notes of A, B, and C respectively.
In the transaction, each gives 2 notes to the other two (loses 4 notes, gains 2 from each of the others).
Final Amounts:
- A: $5x - (4 \times 5) + (2 \times 10) + (2 \times 20) = 5x + 40$.
- B: $10y - (4 \times 10) + (2 \times 5) + (2 \times 20) = 10y + 10$.
- C: $20z - (4 \times 20) + (2 \times 5) + (2 \times 10) = 20z - 50$.
Setting them equal: $5x + 40 = 10y + 10 = 20z - 50$.
Testing the options shows no sets satisfy this equation:
- For (a): $295 \neq 280 \neq 250$.
- For (b): $195 \neq 180 \neq 150$.
- For (c): $235 \neq 220 \neq 190$.
Therefore, the answer is "None of the above".

Question 48

English: There are some flowers in a basket and after every minute they double in size. After 30 minutes the basket is full, then after how many minutes the basket was half full?

Hindi: एक टोकरी में कुछ फूल है और हर मिनट बाद वे दुगने हो जाते हैं। 30 मिनट बाद टोकरी भर जाती है, तो कितने मिनट बाद टोकरी आधी भरी हुई थी ?

(a) 15 मिनट

(b) 20 मिनट

(d) 12 मिनट

Answer: (c) 29 मिनट

Explanation: Since the volume of flowers doubles every minute, the basket is half full exactly 1 minute before it gets completely filled (at 29 minutes).

Question 49

English: It takes 20 days to fill a pond completely. If the water level of the pond doubles every day, then how many days will it take to fill half of the pond?

Hindi: एक तालाब को पूरा भरने में 20 दिन लगते हैं। यदि प्रतिदिन तालाब का जल स्तर दुगुना हो जाता है, तो तालाब को आधा भरने में कितने दिन लगेंगे?

(a) 5 दिन

(b) 10 दिन

(d) 19 दिन

Answer: (d) 19 दिन

Explanation: The water level doubles each day. It is completely filled on Day 20, so it must be half full on Day 19.

Question 50

English: Let it be assumed that the moon completes a complete cycle of the earth in 30 days. If it rises at 6:48 in the east on the first day, then at what time will it rise on the fourth day?

Hindi: यह माना जाये कि चन्द्रमा पृथ्वी के 30 दिन में पूरा चक्र लगाता है। यदि यह पहले दिन पूर्व में 6 बजकर 48 मिनट पर उदय होता है तो चौथे दिन यह किस समय पर उदय होगा?

(a) 8.24 बजे

(b) 9.12 बजे

(d) 11.48 बजे

Answer: (b) 9.12 बजे

Explanation:

The moon completes a full cycle ($360^\circ$) around the Earth in 30 days.
Daily angular eastward shift of the moon = $\frac{360^\circ}{30} = 12^\circ$.
Since Earth rotates $360^\circ$ in 24 hours ($1440\text{ minutes}$), it rotates $1^\circ$ every $4\text{ minutes}$.
Therefore, the moon rises later each day by $12^\circ \times 4\text{ minutes} = 48\text{ minutes}$.
On the 4th day (3 days of delay from Day 1):
$$\text{Total Delay} = 3 \times 48\text{ minutes} = 144\text{ minutes} = 2\text{ hours and } 24\text{ minutes}$$
New rise time = $6:48 + 2\text{ hours and } 24\text{ minutes} = 9:12$.

Numeric