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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.

(3) Comment(s)

Sravan Reddy


As ratio of two numbers is 7:11, and the numbers are whole numbers, the difference is always a multiple of 4. Hence the difference of ages must be 4 or 8 or on. But in options only 8 is given so that is the answer.

Logic for the ratio: If two numbers are 7:11, then we generally take them as 7x and 11x. So, the difference of their ages is 11x-7x=4x (which is a multiple of 4).

P.S. This works for age related problems because we know that their ages will generally won't be in fractions. But this may not work in general algebra as x may be in fractions which makes the number not a multiple of 4.

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.


kindly explain your logic clearly Sravan