# The ages of A and B are presently in the ratio of 5 : 6 respectively. Six years hence, this ratio became 6 : 7 respectively. What was B's age 5 years ago ?

• 125 years
• 230 years
• 331 years
• 436 years
Explanation:-

Solution:
Let A's age be 5x years.
Then, B's age = 6 years
$\begin{array}{rl}& \therefore \frac{5x+6}{6x+6}\\ & ⇒7\left(5x+6\right)=6\left(6x+6\right)\\ & ⇒35x+42=36x+36\\ & ⇒x=6\end{array}$

B's age 5 years ago = (6x - 5) years
= (6 × 6 - 5) years
= 31 years

$\begin{array}{rl}& \therefore \frac{5x+6}{6x+6}\\ & ⇒7\left(5x+6\right)=6\left(6x+6\right)\\ & ⇒35x+42=36x+36\\ & ⇒x=6\end{array}$