# Problems on Ages

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Problems on Ages:

# Aptitude Questions (Problems on Ages):

1. Sanjay is younger than Raj by 4 years. If their ages are in the respective ratio of 7:9, how old Sanjay is?

A)    14 years

B)    18 years

C)    28 years

D)    24.5 years

E)    None of these

Explanation:

Let Raj’s age be x years. Then, Sanjay’s age = (x – 7) years

∴ (x-7)/x = (7/9) <=> 9x – 63 = 7x <=> 2x = 63 <=> x = 31.5

Hence, Sanjay’s age = (x – 7) = 24.5 years

2. The ratio between the present ages of X and Y is 5:7 respectively. If the difference between Y’s present age and X’s age after 6 years is 2, what is the total of X’s and Y’s present ages?

A)    48 years

B)    52 years

C)    56 years

D)    60 years

E)    None of these

Explanation:

Let the present ages of X and Y be 5x years and 7x years respectively.

Then, 7x – (5x + 6) = 2 <=> 2x = 8 <=> x = 4

∴ Required sum = 5x + 7x = 12x = 48 years.

3. Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X’s present age in years?

A)    35

B)    42

C)    49

D)    54

E)    None of these

Explanation:

Let the present ages of X and Y be 5x years and 6x years respectively.

Then, (5x+7)/(6x+7) = (6/7) <=> 7(5x + 7) = 6(6x + 7) <=> x = 7

∴ X’s present age = 5x = 35 years.

4. Eight years ago, the ratio of the ages of K and S was 7:6. Four years hence, the ratio of their ages will be 11:10. What is S’s age at present?

A)    26 years

B)    28 years

C)    20 years

D)    24 years

E)    None of these

Explanation:

Let the ages of K and S 8 years ago be 7x and 6x years respectively.

Then, ((7x+8)+ 4) / ((6x+8)+ 4)) = (11/10) <=> 10(7x + 12) = 11(6x + 12) <=> 4x = 12  x = 3

∴ S’s present age = (6x + 8) = 26 years.

5. The ratio of the present ages of two brothers is 1 : 2 and 5 years back, the ratio was 1 : 3. What will be the ratio of their ages after 6 years?

A)    1 : 4

B)    2 : 3

C)    3 : 5

D)    5 : 6

E) None of these

Explanation:

Let us consider the present ages of the two brothers be x years and 2x years respectively.

Then, (x-6/2x-6) = (1/3) <=> 3(x – 6) = (2x – 6) <=> x = 12

∴ Required rate = (x + 6) : (2x + 6) = 18:30 = 3:5