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Question 46

A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days $$\frac{4}{7}$$ of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?

Solution

Using, $$\frac{M_1D_1H_1}{W_1}$$ $$=\frac{M_2D_2H_2}{W_2}$$

Initially, 117 men completed $$\frac{4}{7}$$ work in 33 days working 8 hours per day. Let $$x$$ men complete the remaining $$\frac{3}{7}$$ work in 13 days working 9 hours per day.

=> $$\frac{117\times33\times8}{4}=\frac{x\times13\times9}{3}$$

=> $$x=33\times2\times3=198$$

$$\therefore$$ Additional men required = $$198-117=81$$

=> Ans - (B)

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