Question

The sum of age of Mena and rekha is 31 years .after 10 years the ratio of their ages will be 8:9 find the present age.

Answer 1

Mena's present age is 14 years and Rekha's present age is 17 years.

• Let the present age of Mena and rekha be x and y  respectively.
• Now, sum of ages of Mena and Rekha is 31 years.

x+y =31  (Equation 1)

• After 10 years , the ratio of their age is 8:9.

$\frac{x+10}{y+10}$ = $\frac{8}{9}$

• Applying componendo on both sides of the equation,

$\frac{x+10+y+10}{y+10}$ = $\frac{8+9}{9}$

$\frac{x+y+20}{y+10}$ = $\frac{17}{9}$

• Now, from equation 1 , substituting the value of x+y

$\frac{31+20}{y+10}$ = $\frac{17}{9}$

$9(\frac{51}{17})$ = y+10

27 = y +10

y = 17.

• Rekha's present age is 17 years.

• Now, substituting the value of y in equation 1,

x = 31 - 17 = 14 years.

• Mena's present age is 14 years.