Question

Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

(A) 11/12
(B) 13/17
(C) 13/19
(D) 12/19
(E) 11/19

Answer 1

Ratio of Quentin new income to Sam new income is
`(11)/(12)`

So option (a) will be correct option

Explanation:

Let Rex income is 100

Then Paul income is 40 % less than Rex income 100 - 100×0.4 = 100-40 = 60

And Quentin's income is 20 % less than Paul income

So Quentin's income is 60 - 60×0.2 = 60-12 = 48

Sam income is 40% less than Paul income

So Sam income = 60 - 60×0.4 = 60 - 24 = 36

Now Rex give 60% income Sam

So Sam new income = 36 + 100×0.6 = 60+36 = 96

And Rex give 40% of his income to Quentin's

So Quentin's new income = 48 + 100×0.4 = 40+48 = 88

Now ratio of Quentin's new income to the Sam new income
`=(88)/(96)=(11)/(12)`

So option (a) will be correct answer