Question

Six years ago the ratio of ages of kamal mahendra Was 6:5, fours years hence the ratio of their ages will be 11:10. What is Mahendra's age at present?

Answer 1

Let current ages be K and M.

5(K-6) = 6(M-6); therefore 5K-30 = 6M-36 and 5K - 6M = -6; 6M-5K = 6

10(K+4) = 11(M+4)

10K + 40 = 11M +44; and 11M - 10K = -4 or 10K - 11 M = 4----(1)

12M-10K = 12----(2).  Adding (1) and (2), M = 16 and K = 18

Answer 2

The ratio of their present ages is 9 : 8

Given:-

• six the year ago ratio of age of kamal and Mahendra 6:5
• four the year hence ratio of their age 11:10

To Find:-

• What is ratio of their present ages.

Assumptions:-

• Let the present age of kamal six years ago be 6x
• Let the present age of Mahendra six years ago be 5x

The present ages will be :-

• The present of of kamal will be 6x + 6 years
• The present age of Mahendra will be 5x + 6 years

The age after four years will be :-

• The age of kamal after 4 years = 6x + 10
• The age of Mahendra after 4 years = 5x + 10

According to the question:-

$\longrightarrow \tt \dfrac{6x+ 10}{5x + 10} = \dfrac{11}{10}$

Cross Multiplying we get :-

$\longrightarrow \tt 10 ( 6x + 10 ) = 11 ( 5x + 10 )$

$\longrightarrow \tt 60x + 100 = 55x + 110$

$\longrightarrow \tt 60x - 55x = 110 - 100$

Solving it further we get :-

$\longrightarrow \tt 5x = 10$

$\longrightarrow \tt x = \cancel\dfrac{10}{5}$

$\longrightarrow \tt {\blue{\boxed{\frak{ x = 2}}}\pink\bigstar}$

The present ages of them will be:-

• kamal ' s age = 6x + 6 = 18 years
• mahendra's age = 5x + 6 = 16 years

The present ratio will be :-

$\longrightarrow \tt 18 : 16$

$\longrightarrow {\boxed{\tt {9 : 8}}}$

Therefore :-

The ratio of their present ages is 9 : 8

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