Question

X alone can do a piece of work in 6 days and y alone in 8 days. X and Y undertook the work for $4800. With the help of Z , they completed the work in 3 days . How much is Z's share

Answer 1

Z’s share is $ 600.

Step-by-step explanation:

Step 1:

X alone can do a piece of work in 6 days

So, work done by X in 1 day = 1/6

Y alone can do a piece of work in 8 days

So, work done by Y in 1 day = 1/8

Let Z alone can do the piece of work in “a” days.

So, work done by Z in 1 day = 1/x

It is also given that, with the help of Z, X and Y can do the piece of work in 3 days

So, work done by X+Y+Z in 1 day = 1/3

Therefore, we can write the eq. as,  

1/6 + 1/8 + 1/a = 1/3

⇒ 1/a = 1/3 – 1/8 – 1/6

⇒ 1/a = [8 – 3 - 4]/24

⇒ 1/a = 1/24

⇒ a = 24 days

Step 2:

X and Y undertook the work for $4800 (given)

We know that the wages are shared on the basis of work done and the work done is reciprocal of the time taken to do that work, therefore,

The ratio of work done by X, Y & Z = 1/6 : 1/8 : 1/24 = 4:3:1

Thus,

The share of Z from the total money will be,

= $\frac{1}{(4+3+1)}$ × 4800

= $\frac{1}{8}$ × 4800

= $600

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Also View:

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Answer 2

Answer:

z receivea the share of rs.600

I have also uploaded the pic to make you understand