Question 74

A can do 50% more work as B can do in the same time. B alone can do a piece of work in 20 hours. A, with help of B, can finish the same work in how many hours?

Solution

Work done by B in hour is given by $$\frac{1}{20}$$

As A can do 50% more efficient than B,

$$\frac{1}{A} = 150 % of \frac{1}{B}$$

$$\frac{1}{A} = \frac{3}{2} \times \frac{1}{B}$$ 

$$\frac{1}{A} =  \frac{3}{2} \times \frac{1}{20}$$

$$A = \frac{3}{40}$$

Work done by A and B together in hour = $$\frac{1}{A} + \frac{1}{B}$$ 

$$\Rightarrow \frac{3}{40} + \frac{1}{20}$$ 

$$\Rightarrow \frac{3 + 2}{40} = \frac{1}{8}$$ 

Total work done by A and B together = 8 hours.

Hence, option B is the correct answer.


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