Question

The ages of Anjali and Renu are in the ratio of 6 : 7 respectively. After 6 years, the ratio of their ages will be 15 : 17. What is the age of Renu?
A) 28
B) 24
C) 32
D) 42

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

Option A) 28

Renu's age is 28

$\textbf{\underline{\underline{Explanation :- }}}$

Given :

The present age ratio = 6 : 7

After 6 years ratio will become = 15 : 7

To find :

The age of Renu

Solution :

Consider the age of Anjali as 6x

Consider the age Renu as 7x

$\star$Equation -

${\boxed{\sf\:{ \frac{6x + 6}{7x + 6} = \frac{15}{17} }}}$

$\sf\star{\implies}17(6x + 6) = 15(7x + 6)$

$\sf\star{\implies}102x +102 = 105x + 90$

$\sf\star{\implies}102x - 105x = 90 - 102$

$\sf\star{\implies} - 3x = - 12$

$\sf\star{\implies} \cancel{-} \: 3x = {\cancel{-}} \: 12$

$\sf\star{\implies} x = \dfrac{12}{3}$

$\sf\star{\implies} x = 4$

Value of 6x

$\sf\star{\implies} 6 \times x$

$\sf\star{\implies} 6 \times 4$

$\sf\star{\implies} 24$

$\boxed{\sf{Anjali \: is \: 24 \: years \: old}}$

Value of 7x

$\sf\star{\implies} 7 \times x$

$\sf\star{\implies} 7 \times 4$

$\sf\star{\implies} 28$

$\boxed{\sf{Renu\: is \: 28 \: years \: old}}$

Renu's age is 28 years.

Therefore, The answer is

Option A)

28 years