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A alone can complete a work in 12 days and B alone in 48 days. Starting with B, they work on alternate days. The total work will be completed in
- A18
- B19
- C\(19\frac{1}{2}\)
- DData insufficient
Answer not set
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CCommunity
(A + B)’s 2 day’s work $( = \frac{1}{{12}} + \frac{1}{{48}} = \frac{5}{{48}})$
Work done in 9 pairs of days $( = \left\{ {\frac{5}{{48}} \times 9} \right\} = \frac{{15}}{{16}})$
Remaining work $( = \left\{ {1 - \frac{{15}}{{16}}} \right\} = \frac{1}{{16}})$
Work done by B on 19th day $(= \frac{1}{{48}})$
Remaining work $( = \left\{ {\frac{1}{{16}} - \frac{1}{{48}}} \right\} = \frac{1}{{24}})$
Now, $(\frac{1}{{12}})$ work is done by A in 1 day.
$(\frac{1}{{24}})$ work is done by A in $( = \left\{ {12 \times \frac{1}{{24}}} \right\} = \frac{1}{2})$
Total time taken $( = 19\frac{1}{2})$
Work done in 9 pairs of days $( = \left\{ {\frac{5}{{48}} \times 9} \right\} = \frac{{15}}{{16}})$
Remaining work $( = \left\{ {1 - \frac{{15}}{{16}}} \right\} = \frac{1}{{16}})$
Work done by B on 19th day $(= \frac{1}{{48}})$
Remaining work $( = \left\{ {\frac{1}{{16}} - \frac{1}{{48}}} \right\} = \frac{1}{{24}})$
Now, $(\frac{1}{{12}})$ work is done by A in 1 day.
$(\frac{1}{{24}})$ work is done by A in $( = \left\{ {12 \times \frac{1}{{24}}} \right\} = \frac{1}{2})$
Total time taken $( = 19\frac{1}{2})$