Question

The ratio of income of A and B is 5:4 and ratio of expenditure is 3:2. If at the end of year, each saves rs.16000 then find the income of A.

Answer 1

Step-by-step explanation:

Let income of A be ₹ x

then, expenditure of A is ₹( x-16000)

Similarly let income of B be ₹ y

then, expenditure of B is ₹ (y-16000)

Given

$\frac{x}{y} = \frac{5}{4 }$

it implies that

$y = \frac{4x}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (1)$

also given that

$\frac{x - 16000}{y - 16000} = \frac{3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (2)$

substituting (1) in (2), we get

$\frac{x - 16000}{( \frac{4x}{5} - 16000) } = \frac{3}{2}$

simplifying, we get

$x - 16000 = \frac{3}{2} ( \frac{4x}{5} - 16000)$

$x - 16000 = \frac{6}{5}x - 24000$

$x - \frac{6}{5} x = - 8000$

$\frac{x}{5} = 8000$

hence

$x = 40000$

thus, income of A is ₹40000

$\frac{x - 16000}{y - 16000} = \frac{3}{2}$

Answer 2

Answer:

Step-by-step explanation:

Let their income be x and expenditure be y.

A

′

s income =5x

B

′

s income =4x

A

′

s expenditure =3y

B

′

s expenditure =2y

Save money =Rs.1600

⇒ Income - expenditure = saves

⇒ 5x−3y=1600 ---- ( 1 )

⇒ 4x−2y=1600 --- ( 2 )

Multiply equation ( 1 ) by 2 and equation ( 2 ) by 3, we get,

⇒ 10x−6y=3200 ---- ( 3 )

⇒ 12x−6y=4800 ---- ( 4 )

By subtracting ( 4 ) from ( 1 ) we get,

⇒ x=800

⇒ Income of A=5x=5×800=Rs.4000