Question

One year ago, Promila was four times as old as her sister Sakshi. Six years hence, Promila's age will exceed her sister's age by $9$ years. The ratio of the present ages of Promila and her sister is

• A. $9:2$
• B. $11:3$
• C. $12:5$
• D. $13:4$

Answer 1

The correct option is D $13:4$

Let Sakshi's age $1$ year ago be $x$ years. Then, Promila's age $1$ year ago $=4x$ years.
$\therefore$ Present age of Sakshi $=(x+1)$ years
and present age of Promila $=(4x+1)$ years
According to question,
$(4x+1)+6=(x+1+6)+9$
$\Rightarrow 4x+7=x+16$
$\Rightarrow 3x=9$
$\Rightarrow x=3$
Ratio of present age of Promila and Sakshi
$=\frac{4x+1}{x+1}=\frac{13}{4}=13:4$