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Two men undertook to do a job for Rs 1400. One of them can do it alone in 7 days and the other in 8 days. With the assistance of a boy, they together completed the work in 3 days. How much money did the boy get ? |
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Answer» 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\(\big(\frac{1}{7}+\frac{1}{8}+\frac{1}{X}\big)\) = 1 \(\Rightarrow\) \(\frac{1}{7}+\frac{1}{8}+\frac{1}{X}\) = \(\frac{1}{3}\) \(\Rightarrow\) \(\frac{1}{X}\) = \(\frac{1}{3}-\big(\frac{1}{7}+\frac{1}{8}\big)\) = \(\frac{56-(24+21)}{168}\) = \(\frac{56-45}{168}\) = \(\frac{11}{168}\) \(\therefore\) 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 = \(\frac{11}{56}\) x Rs 1400 = Rs 275 |
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