Problem Solving

Working alone, Sumio can mow a certain field in x hours. Yoko can mow 50% more field in the same time. When the two work together, they are paid m dollars each one. If Sumio decides to pay Yoko n dollars so they would have received the same compensation per field mowed, what is n in terms of m?

A) 1/2 m
B) 1/3 m
C) 1/4 m
D) 1/5 m
E) 1/6 m

OA: D

Thanks,
Fambrini

Sumio mow certain field in x hours be = y
Yoko mow 3/2y of the field in y hour
sumio gave y dollars to yoko = > m-n = m+n
compensations per field is same for both =>

m-n/y = m+n/3/2y
3m-3n = 2m-2n
m = 5n
n = 1/5
so D

There's a much easier way of solving this.

Suppose that Sumio's rate = s. Then Yoko's rate = 1.5s.

When they work together, Yoko does 1.5s / (s + 1.5s) of the work, or 60%, but only gets 50% of the money.

To fix this, Sumio needs to give Yoko 10% of the money. Sumio has 50% of the money right now, so Sumio must pay Yoko 1/5 of his money (10% of the total / 50% of the total = 1/5).

Thus the answer is (1/5) * Sumio's money, or D.