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Question

$$A$$ is thrice as good as workman as $$B$$ and therefore is able to finish a job in $$60$$ days less than $$B$$. Working together, they can do it in:


A
20 days
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B
2212 days
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C
25 days
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D
30 days
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Solution

The correct option is B $$22\cfrac{1}{2}$$ days
Ratio of times taken by $$A$$ and $$B$$ $$=1:3$$
The time difference is $$(3-1)2$$ days while $$B$$ takes $$3$$ days and $$A$$ takes $$1$$ day.
If difference of time is $$2$$ days, $$B$$ takes $$3$$ days.
If difference of time is  $$60$$ days, $$B$$ takes $$\left( \cfrac { 3 }{ 2 } \times 60 \right) =90$$ days.
So, $$A$$ takes $$30$$ days to do the work.
$$A$$'s $$1$$ day's work $$=\cfrac{1}{30}$$
$$B$$'s $$1$$ day's work $$=\cfrac{1}{90}$$
$$(A+B)$$'s $$1$$ day's work $$=\left( \cfrac { 1 }{ 30 } +\cfrac { 1 }{ 90 }  \right) =\cfrac { 4 }{ 90 } =\cfrac { 2 }{ 45 } $$
$$\therefore$$ $$A$$ and $$B$$ can do the work in $$\cfrac{45}{2}=22\cfrac{1}{2}$$ days.

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