Question 1

Relative ages (chain of differences): Determine how many years older C is than D.  Relations: A is 3 years older than B and 3 years younger than C. B and D are twins (same age).  Find C − D (years older). Choose the correct value.

Accepted Answer

Let ages Let B = D (twins). Then A = B + 3 and C = A + 3 = B + 6. Difference C − D = (B + 6) − B = 6.

Question 2

Heads and legs puzzle (systems with animals): Determine the count of peacocks.  In a zoo there are deer and peacocks. Total heads = 80 (deer + peacocks). Total legs = 200 (deer have 4 legs; peacocks have 2 legs).  Find the number of peacocks. Choose…

Accepted Answer

Let d = deer, p = peacocks. Equations d + p = 80. 4d + 2p = 200 ⇒ divide by 2: 2d + p = 100. Solve (2d + p) − (d + p) = 100 − 80 ⇒ d = 20. Then p = 80 − 20 = 60.

Question 3

Card distribution puzzle (simultaneous linear equations): Find the exact number of cards with C.  Statements: If B gives A 3 cards, then B will have as many as A has now. If D takes 5 cards from B, D will have as many as E has now. A + C together eq…

Accepted Answer

Let counts A = a, B = b, C = c, D = d, E = e. Translate statements 1) B gives A 3 ⇒ b − 3 = a. 2) D takes 5 from B ⇒ d + 5 = e. 3) a + c = 2e. 4) b + d = a + c. 5) a + b + c + d + e = 150. Express in one variable From 1: b = a + 3. From 2: e = d + 5. From 3: c = 2e − a = 2(d + 5) − a = 2d + 10 − a. From 4: (a + 3) + d = a + c ⇒ c = d + 3. Equate c: d + 3 = 2d + 10 − a ⇒ a = d + 7. Then b = d + 10, c = d + 3, e = d + 5. Use total a + b + c + d + e = (d + 7) + (d + 10) + (d + 3) + d + (d + 5) = 5d + 25 = 150. Solve: 5d = 125 ⇒ d = 25 ⇒ c = d + 3 = 28.

Question 4

People and horses (legs on the ground): Infer the number of horses from total legs counted.  There are as many men as horses. Half of the owners (men) are mounted; the rest walk, leading their horses. Total legs on the ground counted = 70.  Find how…

Accepted Answer

Let n = number of horses = number of men. Count legs on the ground Men walking = n/2 ⇒ human legs on ground = (n/2) × 2 = n. All horses have 4 legs on ground regardless of riders ⇒ horse legs = 4n. Total ground legs = n + 4n = 5n = 70. Solve 5n = 70 ⇒ n = 14. Common pitfalls Subtracting legs for mounted horses; a mounted horse still contributes four legs on the ground.

Question 5

Finger-counting (back-and-forth on one hand): Determine the landing finger at a large count.  Counting pattern on the left hand: thumb = 1, index = 2, middle = 3, ring = 4, little = 5; then reverse direction (ring = 6, middle = 7, index = 8), and co…

Accepted Answer

Given data Forward: Thumb(1), Index(2), Middle(3), Ring(4), Little(5) Reverse: Ring(6), Middle(7), Index(8), then Thumb(9) and repeat. Concept/Approach The sequence of landing fingers repeats every 8 counts: [Thumb, Index, Middle, Ring, Little, Ring, Middle, Index]. Reduce 1994 modulo 8. Step-by-step calculation 1994 ÷ 8 = 249 remainder 2.Remainder 2 corresponds to the 2nd item in the 8-step cycle → Index finger. Verification Counts 1–9 land on: T, I, M, R, L, R, M, I, T → cycle matches analysis. Final Answer Index finger

Question 6

Mixed-category word puzzle (sparrows–pigeons–ducks): Compute the total birds from “all … but six” clues. A shooter says: “There were all sparrows but six, all pigeons but six, and all ducks but six in the bag.” Treat the …

Accepted Answer

Let totals be Total = T; counts: S (sparrows), P (pigeons), D (ducks). Translate statements “All sparrows but six” ⇒ non-sparrows = 6 ⇒ T − S = 6.Similarly, T − P = 6 and T − D = 6.Hence S = P = D = T − 6 (all three equal). Compute T = S + P + D = 3(T − 6) ⇒ T = 3T − 18 ⇒ 2T = 18 ⇒ T = 9. Final Answer 9

Question 7

Family ages at birth (multi-relation): Find the sister’s age when Rahul was born.  At Rahul’s birth: Father was 32 years older than Rahul’s brother; Mother was 25 years older than Rahul’s sister. Given now (at birth context): Rahul’s brother is 6 ye…

Accepted Answer

Set ages at Rahul’s birth Rahul = 0. Brother = 6 (given “6 years older”). Father = Brother + 32 = 6 + 32 = 38. Mother = Father − 3 = 35. Sister’s age Mother was 25 years older than sister ⇒ Sister = 35 − 25 = 10. Final Answer 10 years

Question 8

Minimum-count arrangement (ducks in line): Satisfy three positional descriptions simultaneously.  Requirement: “Two ducks in front of a duck”, “two ducks behind a duck”, and “a duck between two ducks”. Find the smallest number of ducks that can sati…

Accepted Answer

Visualize 3 ducks in a row D₁ — D₂ — D₃ Check conditions Two in front of a duck: for D₃, ducks D₁ and D₂ are in front. Two behind a duck: for D₁, ducks D₂ and D₃ are behind. A duck between two ducks: D₂ is between D₁ and D₃. Conclusion All three statements hold with just 3 ducks; fewer is impossible. Final Answer 3

Question 9

Knockout tournament (singles): Find the minimum matches to determine a winner among 30 players.  Rules: One loss eliminates a player (single-elimination); no ties. How many matches are needed at minimum to produce a single champion? Choose the corre…

Accepted Answer

Concept/Approach Each match eliminates exactly one player. To go from 30 players to 1 winner, 29 eliminations must occur. Calculation Matches needed = Players − 1 = 30 − 1 = 29. Final Answer 29

Question 10

After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equal distribution. What was the total number of sweets?

Accepted Answer

Let the total number of sweets be (25x + 8). Then, (25x + 8) - 22 is divisible by 28 ⟺ (25x - 14) is divisible by 28 ⟺ 28x - (3x + 14) is divisible by 28 ⟺ (3x + 14) is divisible by 28 ⟺ x = 14. Therefore Total number of sweets = (25 x 14 + 8) = 358.

Question 11

Between two book-ends in your study are displayed your five favourite puzzle books. If you decide to arrange the five books in every possible combination and moved just one book every minute, how long would it take you?

Accepted Answer

Clearly, number of ways of arranging 5 books = 5 ! = 5 x 4 x 3 x 2 x 1 = 120. So, total time taken = 120 minutes = 2 hours.

Question 12

First bunch of bananas has (1/4) again as many bananas as a second bunch. If the second bunch has 3 bananas less than the first bunch, then the number of bananas in the first bunch is

Accepted Answer

Question 13

In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is

Accepted Answer

Let the number of cows be x and the number of hens be y. Then, 4x + 2y = 2 (x + y) + 14 ⟺ 4x + 2y = 2x + 2y + 14 ⟺ 2x = 14 ⟺ x = 7.

Question 14

A number consists of two digits whose sum is 11. If 27 is added to the number, then the digits change their places. What is the number?

Accepted Answer

Let the ten's digit be x. Then, unit's digit = (11 - x). So, number = 10x + (11 - x) = 9x + 11. Therefore (9x + 11) + 27 = 10 (11 - x) + x ⟺ 9x + 38 = 110 - 9x ⟺ 18x = 72 ⟺ x = 4. Thus, ten's digit = 4 and unit's digit = 7. Hence, required number = 47.

Question 15

At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether?

Accepted Answer

Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45.

Question 16

A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 8.00 a.m., at what time will he first touch a flag a…

Accepted Answer

Net ascent of the monkey in 1 hour = (30 - 20) feet = 10 feet. So, the monkey ascends 90 feet in 9 hours i.e. till 5 p.m. Clearly, in the next 1 hour i.e. till 6 p.m. the monkey ascends remaining 30 feet to touch the flag.

Question 17

In a class, 3/5 of the students are girls and rest are boys. If 2/9 of the girls and 1/4 of the boys are absent, what part of the total number of students is present?

Accepted Answer

Question 18

A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is

Accepted Answer

Clearly, out of every 16 persons, there is one captain. So, number of captains (1200/16) = 75.

Question 19

If a clock takes seven seconds to strike seven, how long will it take to strike ten?

Accepted Answer

Question 20

Aruna cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight. If she has seven pieces of the cake in all with her, how heavy was the original cake?

Accepted Answer

The seven pieces consist of 6 smaller equal pieces and one half cake piece. Weight of each small piece = 20 g. So, total weight of the cake = [2 x (20 x6)]g= 240 g.

Arithmetic Reasoning Questions