Question

The ratio of the incomes of a and b is 5 : 4 and the ratio of their expenditures is 3 : 2. if at the end of the year, each saves rs. 1600, then the income of a is :

Answer 1

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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

Both saves 1600

Income - expenditure = saves

5x - 3y = 1600 .... ( i ) × 2

4x - 2y = 1600 .... ( ii ) × 3

Sub ( ii ) × 2 from ( i ) × 3

10x - 6y - ( 12x - 6y ) = 3200 - 4800

10x - 6y - 12x + 6y = - 1600

- 2x = - 1600

x = 800

Putting the value of x in ( i )

5x - 3y = 1600

4000 - 3y = 1600

- 3y = - 2400

y = 800

Income of a :- 5x = 4000

Answer 2

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