Question

Two men undertake to do a piece of work for Rs 600. One alone could do it in 6 days and the other in 8 days. With the assistance of a boy they finish it in 3 days. Boy's share should be

• A. Rs 75
• B. Rs 225
• C. Rs 300
• D. Rs 100

Answer 1

The Correct Option is A

Let the boy take b days to complete the work
So,
\(\Rightarrow\;\)\(\frac{1}{6} + \frac{1}{8} + \frac{1}{b} = \frac{1}{3}\)
\(\Rightarrow\;\)\(\frac{1}{b} = \frac{1}{24}\)
\(\Rightarrow\;\)b = 24 days
Amount divided in inverse ratio of number of days taken, so
Days ratio = \(6:8:24\)
Inverse ratio of amount divison = \(\frac{1}{6}:\frac{1}{8}:\frac{1}{24} = 4:3:1\)
Boy's share = \(\frac{1}{8} \times 600 = Rs. 75\)

The correct option is (A): Rs 75