Question

The ratio of the incomes of P and Q is `5:4.` The ratio of their expenditure is `4:3` The savings of P more then that of Q by `16(2)/(3)%.` What percentage of his income does P spend ?
A. `52(2)/(3)%`
B. `53(1)/(3)%`
C. `54(1)/(3)%`
D. `51(2)/(3)%`

Answer 1

Correct Answer - B
Let the incomes of P and Q be Rs 5x and Rs 4x respectively . Let the expenditure of P and Q be Rs 4y and Rs 3y respectively
Saving of P =Rs(5x-4y)
Savings of Q =Rs(4x-3y)
`therefore 5x-4y=(4x-3y)(1+(16(2)/(3))/(100))`
`implies 5x-4y =(4x-3y)((7)/(6))`
`implies 30x-24y=28x-21y`
`implies 2x=3y`
Required percentage `=(4y)/(5x)(100)`
`=(4)/(3)((2)/(3))(100)=53(1)/(3)%`