Quentin's income is 60% less than Rex's income, and Sam's income is 25

Option A

Q = 0.4R
S = 0.75Q = 0.75*0.4R = 0.3R
New Income:
Q = 0.4R + 0.4R = 0.8R
S = 0.3R + 0.6R = 0.9R

Q/S =8/9

Let Rex's income be 100, so the first statement would be :
Rex : 100
Quentin : 40
Sam : 30
Then, Rex gave 60% of his income to Sam and 40% of his income to Quentin. So the new incomes are :
Rex : 0
Quentin: 80
Sam :90
So
The ratio is : Q/S = 80/90 = 8/9

Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin'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. 8/9
B. 11/12
C. 8/13
D. 11/13
E. 12/13

Let Rex's income be = 100
Quentin's income = 60% less than Rex's income = 40% of 100 = 40
Sam's income = 25% less than Quentin's income = 75% of 40 = \(\frac{75}{100}\) x 40 = 30

Rex gave 60% of his income to Sam = 60% of 100 = \(\frac{60}{100}\) x 100 = 60
Sam's new income = 30 + 60 = 90

Rex gave 40% of his income to Quentin = 40% of 100 = \(\frac{40}{100}\) x 100 = 40
Quentin's new income = 40 + 40 = 80

Required fraction = Quentin's new income / Sam's new income = \(\frac{80}{90}\) = \(\frac{8}{9}\)
Answer A...

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Is this really a 500 level question? Definitely seems a bit trickier- but anyways

Q= r(2/5) + r(2/5)
S = (3/4)Q + r(3/5)

Let R be 100

Q= 100(2/5) + 100(2/5)=

40 + 40 = 80

S = (3/4) 40 + 100(3/5)

30 + 60 = 90

80/90 = 8/9

Let Rex's income be 100

So, Quentin's income is 40

Tus, Sam's income is 3/4*40 = 30


Sam's new income = 30 + 60 = 90
Quentin's new income = 40 + 40 = 80

Thus, the new fraction is 80/90 = 8/9, Answer must be (A)

If we let Rex’s income be $10, then Quentin’s income is $4 and Sam’s income is $3. If Rex gives $6 to Sam and $4 to Quentin, then Quentin’s new income is $8 and Sam’s is $9. Therefore, Quentin’s new income is 8/9 of Sam’s new income.

Answer: A

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