Question

Q15. Present ages of Vikas and Raman are in the ratio of 6:5 respectively. If the present age of
Rohan is 98 years and the present age of Vikas is 3/7 of the the present age of Rohan, then after
how many years the ages of Vikas and Raman would be in the ratio of 7 : 6?
(a) 6
(b) 7
(C) 5
(d) 8​

Answer 1

Answer:

5 is the answer for this question

Answer 2

Given:-

Age of Rohan = 98

To find:-

After how many years the ages of Vikas and Raman would be in the ratio of 7 : 6

Assumption:-

Let the common multiple of the ratio of present ages of Vikas and Raman be x

Age of Vikas = 6x

Age of Raman = 5x

Solution:-

Age of Raman = 98

$\sf{Age\:of\:Vikas\:= \dfrac{3}{7}\:of\:98}$

= $\sf{Age\:of\:Vikas = \dfrac{3}{7}\times98}$

= $\sf{Age\:of\:Vikas = 42\:years}$

Now,

$\sf { 6x = 42}$

$\sf{\implies x = \dfrac{42}{6}}$

$\sf{\implies x = 7}$

Therefore,

$\sf{Age\: of\: Raman = 5x = 5\times7 = 35\:years}$

Therefore,

Ratio of age of Vikas : Raman = 42 : 35

Now,

Let the year after which age of Vikas and Raman will become 7 : 6 be x

ATQ,

$\sf{\dfrac{42+x}{35+x}= \dfrac{7}{6}}$

= $\sf{6(42+x)= 7(35+x)}$

$\sf{\implies 252 + 6x = 245 + 7x}$

$\sf{\implies 252-245=7x-6x}$

$\sf{\implies x = 7}$

$\sf{\therefore}$ After 7 years, ages of Vikas and Raman will be in the ratio 7 : 6