A) Rs. 250
B) Rs. 275
C) Rs. 300
D) Rs. 325
Correct Answer: D
Solution :
First man's 1 days' work \[=\frac{1}{7}\] Other man's 1 days' work \[=\frac{1}{8}\] Let the boy complete the whole work in x days. Then, Boys' 1 days work \[=\frac{1}{x}\] Given, \[3\left( \frac{1}{7}+\frac{1}{8}+\frac{1}{x} \right)=1\] \[\Rightarrow \,\frac{1}{7}+\frac{1}{8}+\frac{1}{x}=\frac{1}{3}\Rightarrow \,\frac{1}{x}=\frac{1}{3}-\left( \frac{1}{7}+\frac{1}{8} \right)\] \[=\frac{56-(24+21)}{168}=\frac{56-45}{168}=\frac{11}{168}\] \[\therefore \] The boy can complete the work in \[\frac{168}{11}\] days. \[\therefore \] Ratio of their shares = Ratio of their one days' work \[=\frac{1}{7}:\frac{1}{8}:\frac{11}{168}=24:21:11\] \[\therefore \] The boy's share \[=\frac{11}{56}\,\times \,\text{Rs}\,1400\,=\text{Rs}\,275\].
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