Arithmetic Reasoning

Question: A woman says, “If you reverse my own age, the figures represent my husband’s age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum.” The woman’s age is
[A].

23 years

[B].

34 years

[C].

45 years

[D].

None of these

Answer: Option C

Explanation:

Let x and y be the ten’s and unit’s digits respectively of the numeral denoting the woman’s age.

Then, woman’s age = (10X + y) years; husband’s age = (10y + x) years.

Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)

(9y-9x) = (1/11)(11y + 11x) = (x + y) 10x = 8y x = (4/5)y

Clearly, y should be a single-digit multiple of 5, which is 5.

So, x = 4, y = 5.

Hence, woman’s age = 10x + y = 45 years.

Question: A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is
[A].

12

[B].

15

[C].

18

[D].

20

Answer: Option B

Explanation:

Let son’s age be x years. Then, father’s age = (3x) years.

Five years ago, father’s age = (3x – 5) years and son’s age = (x – 5) years.

So, 3x – 5 = 4 (x – 5) 3x – 5 = 4x – 20 x = 15.

Question: A father tells his son, “I was of your present age when you were born”. If the father is 36 now, how old was the boy five years back ?
[A].

13

[B].

15

[C].

17

[D].

20

Answer: Option A

Explanation:

Let the father’s age be x and the son’s age be y.

Then, x – y = y or x = 2y,

Now, x = 36. So, 2y = 36 or y = 18.

Therefore Son’s present age = 18 years.

So, son’s age 5 years ago = 13 years.

Question: A is three times as old as B. C was twice-as old as A four years ago. In four years’ time, A will be 31. What are the present ages of B and C ?
[A].

9, 46

[B].

9, 50

[C].

10, 46

[D].

10, 50

Answer: Option B

Explanation:

We have : A = 3B …(i) and

C – 4 = 2 (A – 4) …(ii)

Also, A + 4 = 31 or A= 31-4 = 27.

Putting A = 27 in (i), we get: B = 9.

Putting A = 27 in (ii), we get C = 50.

Question: Nitin’s age was equal to square of some number last year and the following year it would be cube of a number. If again Nitin’s age has to be equal to the cube of some number, then for how long he will have to wait?
[A].

10 years

[B].

38 years

[C].

39 years

[D].

64 years

Answer: Option B

Explanation:

Clearly, we have to first find two numbers whose difference is 2 and of which the smaller one is a perfect square and the bigger one a perfect cube.

Such numbers are 25 and 27.

Thus, Nitin is now 26 years old. Since the next perfect cube after 27 is 64,

so required time period = (64 – 26) years = 38 years.

Question: Ayush was born two years after his father’s marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ?
[A].

23 years

[B].

25 years

[C].

33 years

[D].

35 years

Answer: Option A

Explanation:

Ayush’s present age = 10 years.

His mother’s present age = (10 + 20) years = 30 years.

Ayush’s father’s present age = (30 + 5) years = 35 years.

Ayush’s father’s age at the time of Ayush’s birth = (35 – 10) years = 25 years.

Therefore Ayush’s father’s age at the time of marriage = (25 – 2) years = 23 years.

Question: 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?
[A].

2

[B].

3

[C].

6

[D].

12

Answer: Option C

Explanation:

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: 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 horses are there ?
[A].

10

[B].

12

[C].

14

[D].

16

Answer: Option C

Explanation:

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: 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
[A].

5

[B].

7

[C].

10

[D].

12

Answer: Option B

Explanation:

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: 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 D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?
[A].

28

[B].

29

[C].

31

[D].

35

Answer: Option A

Explanation:

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.