Question : A can do a piece of work in 8 days, while B can do it in 7 days. If they work at it alternately beginning with A, then in how many days will the work be completed?
Option 1: 8
Option 2: $8 \frac{1}{2}$
Option 3: $7 \frac{1}{2}$
Option 4: 7
Correct Answer: $7 \frac{1}{2}$
Solution :
One day work of A = $\frac{1}{8}$
One day work of B = $\frac{1}{7}$
Working alternatively,
Two day work of A + B = $\frac{1}{8}+\frac{1}{7}$
= $\frac{15}{56}$
Six days work of (A + B) = $3\times\frac{15}{56}$
= $\frac{45}{56}$
On the seventh day, A works and adds his contribution, now work done = $\frac{45}{56}+\frac{1}{8}$
= $\frac{52}{56}$
Remaining work = $1-\frac{52}{56}=\frac{1}{14}$
The remaining work is completed by B on the eighth day with the efficiency of $\frac{1}{7}$= $\frac{\frac{1}{14}}{\frac{1}{7}}$
= $\frac{1}{2}$
Thus, the work is completed in $7\frac{1}{2}$ days
Hence, the correct answer is $7\frac{1}{2}$.
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