Question

Raju is 19 years younger than his cousin. After 5 years, their
ages will be in the ration 2 :3. Find their present ages.
Give STEP BY STEP EXPLANATION too

Answer 1

Given :-

Raju is 19 years younger than his cousin.

Ratio between Raju and his cousin after 5 years = 2 : 3

To Find :-

The present age of Raju.

The present age of Raju's cousin.

Analysis :-

Consider the present ages of Raju and his cousin as variables.

Make an equation where in the case of ages 5 years later.

Then find the value of the variable accordingly.

Solution :-

Let Raju's cousin's age be 'x', then, Raju's present age would be 'x-19'.

After 5 years,

Age of cousin = x + 5 years

Age of Raju = (x - 19) + 5 = x - 14 years

Making an equation,

$\sf (x-19)+\dfrac{5}{x} +5=\dfrac{2}{3}$

$\sf 5 + x - 5 +\dfrac{19}{x} +5=\dfrac{2}{3}$

$\sf 5 + x - \dfrac{14}{x} +5=\dfrac{2}{3}$

$\sf 15 + 3x -\dfrac{42}{2x} +10$

$\sf - 37 + 3x = 2x+10$

$\sf - 37 - 10 = 2x - 3x$

$\sf - 47 = - x$

$\sf x=47$

Raju's present age = 47 years

Cousin's age = x + 5

= 47 + 5 = 52 years

Therefore, Raju's and his cousin's age is 47 and 52 years respectively.

Answer 2

HOPE IT WILL HELP YOU

ANSWER

Let the age of Raju = x

Let the age of Raju = xAge of Raju's cousin = 19 + x

Let the age of Raju = xAge of Raju's cousin = 19 + xAges after 5 years

Let the age of Raju = xAge of Raju's cousin = 19 + xAges after 5 yearsRaju: x + 5

Let the age of Raju = xAge of Raju's cousin = 19 + xAges after 5 yearsRaju: x + 5His cousin: 19 + x + 5 = 24 + x

Let the age of Raju = xAge of Raju's cousin = 19 + xAges after 5 yearsRaju: x + 5His cousin: 19 + x + 5 = 24 + xRatio of their ages = 2:3

Let the age of Raju = xAge of Raju's cousin = 19 + xAges after 5 yearsRaju: x + 5His cousin: 19 + x + 5 = 24 + xRatio of their ages = 2:3Thus, we have

Let the age of Raju = xAge of Raju's cousin = 19 + xAges after 5 yearsRaju: x + 5His cousin: 19 + x + 5 = 24 + xRatio of their ages = 2:3Thus, we haveCross multiplying, we get

Let the age of Raju = xAge of Raju's cousin = 19 + xAges after 5 yearsRaju: x + 5His cousin: 19 + x + 5 = 24 + xRatio of their ages = 2:3Thus, we haveCross multiplying, we get3(x + 5) = 2(24 + x)

Let the age of Raju = xAge of Raju's cousin = 19 + xAges after 5 yearsRaju: x + 5His cousin: 19 + x + 5 = 24 + xRatio of their ages = 2:3Thus, we haveCross multiplying, we get3(x + 5) = 2(24 + x)3x + 15 = 48 + 2x

Let the age of Raju = xAge of Raju's cousin = 19 + xAges after 5 yearsRaju: x + 5His cousin: 19 + x + 5 = 24 + xRatio of their ages = 2:3Thus, we haveCross multiplying, we get3(x + 5) = 2(24 + x)3x + 15 = 48 + 2x3x - 2x = 48 - 15