Question 1

A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?

Accepted Answer

Since B and D are twins, so B = D. Now, A = B + 3 and A = C - 3. Thus, B + 3 = C - 3 ⟺ D + 3 = C-3 ⟺ C - D = 6.

Question 2

There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?

Accepted Answer

Let x and y be the number of deer and peacocks in the zoo respectively. Then, x + y = 80 ...(i) and 4x + 2y = 200 or 2x + y = 100 ...(ii) Solving (i) and (ii), we get) x = 20, y = 60.

Question 3

A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and …

Accepted Answer

Clearly, we have : A = B - 3 ...(i) D + 5 = E ...(ii) A+C = 2E ...(iii) B + D = A+C = 2E ...(iv) A+B + C + D + E=150 ...(v) From (iii), (iv) and (v), we get: 5E = 150 or E = 30. Putting E = 30 in (ii), we get: D = 25. Putting E = 30 and D = 25 in (iv), we get: B = 35. Putting B = 35 in (i), we get: A = 32. Putting A = 32 and E = 30 in (iii), we get: C = 28.

Question 4

A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many hors…

Accepted Answer

Let number of horses = number of men = x. Then, number of legs = 4x + 2 x (x/2) = 5x. So, 5X = 70 or x = 14.

Question 5

A girl counted in the following way on the fingers of her left hand : She started by calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5 and then reversed direction calling the ring finger 6, middle finger 7 and …

Accepted Answer

Clearly, while counting, the numbers associated to the thumb will be : 1, 9,17, 25,..... i.e. numbers of the form (8n + 1). Since 1994 = 249 x 8 + 2, so 1993 shall correspond to the thumb and 1994 to the index finger.

Question 6

A bird shooter was askgd how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?

Accepted Answer

There were all sparrows but six' means that six birds were not sparrows but only pigeons and ducks. Similarly, number of sparrows + number of ducks = 6 and number of sparrows + number of pigeons = 6. This is possible when there are 3 sparrows, 3 pigeons and 3 ducks i.e. 9 birds in all.

Question 7

When Rahul was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rahul's brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he…

Accepted Answer

When Rahul was born, his brother's age = 6 years; his father's age = (6 + 32) years = 38 years, his mother's age = (38 - 3) years = 35 years; his sister's age = (35 - 25) years = 10 years.

Question 8

What is the smallest number of ducks that could swim in this formation - two ducks in front of a duck, two ducks behind a duck and a duck between two ducks?

Accepted Answer

Clearly, the smallest such number is 3. Three ducks can be arranged as shown above to satisfy all the three given conditions.

Question 9

The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner?

Accepted Answer

Clearly, every member except one (i.e. the winner) must lose one game to decide the winner. Thus, minimum number of matches to be played = 30 - 1 = 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