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The ages of Shivali and Tanisha are in the ratio of $11:7$ respectively. After 8 years the ratio of their ages will be $15:11$. What is the difference in years between their ages?


4 year


10 year


6 year


8 year

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Option(D) is correct

Let, the age of Shivali be, $S=11x$ and age of Tanisha be, $T=7x$.

Now, according to question after 8 years the ratio of their age become $\frac{15}{11}$.

$⇒ \dfrac{11x+8}{7x+8}=\dfrac{15}{11}$

$⇒ 121x+88=105x+120$

$⇒ x=2$

Difference in ages $=15×2−11×2$

$=\textbf{8 years}$

Edit: For a quick alternative approach, check comment by Sravan Reddy.

(1) Comment(s)

Sravan Reddy

Slight kill method (took 20 sec):

Ratio - 7:11

So difference 4 or its multiple.

With options 4 or 8. so ages 11,7 or 22, 14.

Later is correct with direct adding 8 and checking.