Question

The ages of rohini and shwetha 5 years ago was in the ratio 1:4 5 years from now tha ratio is 1:2 find the ratio of their ages after 15 years

Answer 1

1:5..............000000

Answer 2

Answer:

The ratio of their ages after 15 years is 5:8

Step-by-step explanation:

Let the age of Rohini is x and the age of Shwetha is y.

Hence, the ages of Rohini and Shewtha 5 years ago was (x-5) and (y-5) respectively.

And the ages of Rohini and Shewtha 5 years from now will be (x+5) and (y+5) respectively.

From the question, we have

$\frac{x-5}{y-5}=\frac{1}{4}\\\\4x-20=y-5\\y=4x-15......(1)$

Also, we have

$\frac{x+5}{y+5}=\frac{1}{2}\\\\2x+10=y+5\\\text{Substitute the value of y from (1)}\\2x+10=4x-15+5\\-2x=-20\\x=10$

Hence, the value of y is

y = 4(10)-15

y = 40-15

y = 25

Hence, the ratio of their ages after 15 years is

$\frac{10+15}{25+15}\\\\\frac{25}{40}\\\\\frac{5}{8}$