Question

The ratio of ages of M and N is 14 : 5. The product of their ages is 304. What will be the ratio of their ages after 4 years?

Answer 1

Answer:

After 4 years, the ratio of their ages be

= 15 * √(152/35) + 4 : 5 * √(152/35) + 4

Solution:

Given,

the ratio of ages of M and N is 14 : 5

Let x be the common multiple. Then age of M is 14x years and that of N is 5x years

ATQ, product of the ages = 304

Then 14x * 5x = 304

or, x² = 304 / 70

or, x² = 152 / 35

or, x = √(152/35)

Therefore age of M is now

= 14 * √(152/35)

and that of N is

= 5 * √(152/35)

After 4 years, the age of M be

= 14 * √(152/35) + 4

and that of N be

= 5 * √(152/35)

Thus the required ratio be

= 15 * √(152/35) + 4 : 5 * √(152/35) + 4

Answer 2

The ratio of ages of M and N after 4 years is "2 : 1".

Step-by-step explanation:

The ratio of the present ages of M and N = 14 : 5 and

The product of their ages = 304

To find, the ratio of ages of M and N after 4 years = ?

After 4 yeras,

The present ages of M = (14 + 4) = 18 years and

The present ages of N = (5 + 4) = 9 years

∴ The ratio of ages of M and N after 4 years

= 18 : 9

Dividing by 9, we get

= $\dfrac{18}{9} :\dfrac{9}{9}$

= 2 : 1

Thus, the ratio of ages of M and N after 4 years is "2 : 1".