Question

X and Y can do a job in 12 days. After working for two days, they are assisted by Z, who works at the same rate as X. The remaining work gets completed in 6-days. In how many days will Y 4 alone do the work? 1​

Answer 1

Question:

X and Y can do a job in 12 days. After working for two days, they are assisted by Z, who works at the same rate as X. The remaining work gets completed in 6-days. In how many days will Y 4 alone do the work?

Solution:

Note First : At X,Y,Z I have Written A,B,C you can change it.

Work done by (A + B) in one day = 1/12 of the whole. ….(1)

Work done by (A+B) in 2 days = 2 × 1/12 = 1/6 of the whole.

Work remaining to be done after (A+B) have worked on it for 2 days = 1 - 1/6 = 5/6.

Now A, and B are joined by C, (who is as as efficient as A ie C =A).

A +B +C finish the remaining 5/6 of the whole work in another 25/4 days

Work done by A +B + C in one day = (5/6) ÷ (25/4) = 2/15 of the whole. Now as C= A,

Work done by 2A + B in one day = 2/15 of the whole ……(2)

Subtracting (1) from (2), we would get the work done by A alone in 1 day.

Work done by A working alone in 1 day =(2/15) -(1/12) = (8–5)/60 = 3/60 = 1/20 of the whole……..(3)

So A working alone could finish the work in 20 days.

Subtracting (3) from (1) we can get work done by B working alone in 1 day

Work done by B in one day = (1/12) -(1/20) = (5–3)/60 = 2/60 = 1/30 of the whole ——-(4).

So working alone B could finish the work in 30 days.

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Answer 2

Step-by-step explanation:

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