Question: A and B together can do a piece of work in 7\displaystyle \frac{1}{2} days and B alone can do it in 25 days. In how many days can A alone finish the work?
(a) 10\displaystyle \frac{5}{7}
(b) 10\displaystyle \frac{4}{7}
(c) 10
(d) None of the above
Ans: (a) 10\displaystyle \frac{5}{7}
Explanation:
\begin{aligned}
\text{Total Work}&=\text{LCM }(7\frac{1}{2},25)\\[1em]
&=\text{LCM }(\frac{15}{2},25)\\[1em]
&=\frac{\text{LCM }(15,25)}{\text{HCF }(2,1)}\\[1em]
&=\frac{75}{1}\\[1em]
&=15 \text{ units}
\end{aligned}
A and B efficiency = \displaystyle \frac{75}{15}\times 2 = 10 units/day
B’s efficiency = \displaystyle \frac{75}{25} = 3 units/day
Now, A’s efficiency = 10 – 3 = 7 units/day
Time taken by A to complete the work
= \displaystyle \frac{75}{7}=10\displaystyle \frac{5}{7} \text{ days}
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