O level math problem?

Question

X can do a piece of work in 10 days, while Y alone can do it in 15. They work together for 5 days and the rest is done by Z in 2 days. If they get £400 for the whole work, how much would each worker get?(Show workings please)

Raj K · Accepted Answer

X can do a piece of work in = 10 days
X can do work in 1 day = 1/10
Y alone can the work in = 15
Y can do work in 1 day = 1/15
X does work in 5 days =5/10=1/2
Y does work in 5 days = 5/15=1/3
Work done by z= 1−(1/2+1/3) =1/6
Total amount = £400
Share of X=£400×(1/2)=£200 
Share of Y=£400×(1/3)=£133.33
Share of Z=£400×(1/6)=£ 66.67

Keith A · Answer

In one day:
X can do  1/10  of the work,
Y can do  1/15  of the work,
    so, together,
x and Y  can do 1/10 + 1/15 of it, i.e., 5/30. = 1/6.
So in  5 days, they achieve  5/6  of the work,
leaving  1/6  for  Z,
who therefore  receives  £400/6 = £66.67.
The remaining  £333.33  should be divided in the ration  3:2  between  X  and  Y.
So  X  gets  £200,  and  Y,  £133.33

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O level math problem?

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