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MI alone can do a work in 14 days and M2 alone can do the same work in 70 days. With help of M3, they finish the same work in 7 days. In how many days
Question

MI alone can do a work in 14 days and M2 alone can do the same work in 70 days. With help of M3, they finish the same work in 7 days. In how many days M3 alone can do the same work?

A.

20 days

B.

17.5 days

C.

19 days

D.

21 days

Correct option is B

Given: MI alone: 14 days, M2 alone: 70 days, M1 + M2 + M3 together: 7 days
Formula Used: Work done per day = 1/Days for each worker
Solution:

Work done by M1 in 1 day = 1/14,

M2 in 1 day = 1/70,

M1 + M2 + M3 in 1 day = 1/7
Let work done by M3 in 1 day = 1/M3 days
114+170+1M3=17570+170+1M3=17670+1M3=171M3=176701M3=10706701M3=4701M3=235M3=352=17.5days\begin{aligned}&\frac{1}{14} + \frac{1}{70} + \frac{1}{M_3} = \frac{1}{7} \\&\frac{5}{70} + \frac{1}{70} + \frac{1}{M_3} = \frac{1}{7} \\&\frac{6}{70} + \frac{1}{M_3} = \frac{1}{7} \\&\frac{1}{M_3} = \frac{1}{7} - \frac{6}{70} \\&\frac{1}{M_3} = \frac{10}{70} - \frac{6}{70} \\&\frac{1}{M_3} = \frac{4}{70} \\&\frac{1}{M_3} = \frac{2}{35} \\&M_3 = \frac{35}{2}= 17.5 days\end{aligned}​​

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