Question

After 10 years, the age of X is twice the age of Y. Before 10 years, the age of x is sixth times the age of Y. Find their ages.​

Answer 1

Question

After 10 years, the age of X is twice the age of Y. Before 10 years, the age of x is sixth times the age of Y. Find their ages.​

Solution

Let the present age of X be x years and the present age of Y be y years.

According to the above question, the following information is given -

After 10 years, the age of X is twice the age of Y. Before 10 years, the age of x is sixth times the age of Y.

After 10 years, the age of X becomes x + 10 years.

Similarly the age of Y becomes y + 10 years.

So,

x + 10 = 2 ( y + 20 )

x + 10 = 2y + 20

x = 2y + 10 ........................ ( 1 )

Before 10 years, the age of X becomes x - 10 years.

Similarly the age of Y becomes y - 10 years.

So,

x - 10 = 6 ( y - 10 )

x - 10 = 6y - 60

x = 6y - 50 .......................... ( 2 )

These equations are equal .

So,

6y - 50 = 2y + 10

4y = 60

y = 15

x = 40

So the present ages of x and y are 40 and 15 years respectively .