Question

The ratio between the ages of appu and ryan at present is 3:4. Five years ago the ratio of their ages was 2:3.What is the present age of appu?

Answer 1

Answer:

The present age of Appu is 15.

Step-by-step explanation:

A- Appu, R - Ryan,

A : R = 3 : 4,  so A = 3 R / 4

( A - 5 ) : ( R - 5 ) = 2 : 3

3 ( A - 5 ) = 2 ( R - 5 )

3 A - 15 = 2 R - 10

3 * 3 R /4 - 2 R = - 10 + 15

9 R/4 - 2 R = 5    /*4

9 R - 8 R = 20

R = 20, A = 3*20 / 4 = 15

Prove :

15 : 20 = 3 : 4,    10 : 15 = 2 : 3.

Answer 2

Answer:

The Present age of Appu is 15 years

Step-by-step explanation:

Let present age of Appu be x and

Present age of Ryan be y

According to first condition,

x : y = 3 : 4

$\frac{x}{y}$ = $\frac{3}{4}$   ( Let this be eqn 1 )

Five years ago the ages will be 5 years less than present,

So,

Five years ago age of Appu = x - 5

Five years ago age of Ryan = y - 5

According to question,

( x - 5 ) : ( y - 5 ) = 2 : 3

$\frac{x-5}{y-5}$ = $\frac{2}{3}$

3 ( x - 5 ) = 2 ( y - 5 )

3x - 15 = 2y - 10

3x - 2y - 15 + 10 = 0

3x - 2y = 5 ( Let this be Eqn 2 )

Now from first equation ,

4x = 3y

x = $\frac{3y}{4}$

Substituting value of x in Eqn 2

3 * ( $\frac{3y}{4}$ ) - 2y = 5

$\frac{9y}{4}$ - 2y = 5

$\frac{9y - 8y}{4}$ = 5

9y - 8y = 20

y = 20

x = $\frac{3y}{4}$

x = $\frac{3 * 20}{4}$

x = 15

Hence,

The Present age of Appu is 15 years