Question

# A is twice as good a workman as B and together they finish a price of work in $$14$$ days. In how many days can A alone finish the work?

A
13
B
15
C
17
D
21

Solution

## The correct option is D $$21$$Let the work done by B be $$x$$.$$\therefore$$Work done by A $$= 2x$$Work done by A and B together in $$14$$ days $$= 1$$Work done by A and B together in $$1$$ day $$=\cfrac{1}{14}$$$$\Rightarrow$$ Work done by A in $$1$$ day $$+$$ Work done by B in $$1$$ day $$=\cfrac{1}{14}$$$$x + 2x = \cfrac{1}{14}$$$$\Rightarrow \; 3x = \cfrac{1}{14}$$$$\Rightarrow \; x = \cfrac{1}{42}$$Work done by B in $$1$$ day $$=\cfrac{1}{42}$$$$\therefore$$ Work done by A in $$1$$ day $$=\cfrac{1}{21}$$Hence, to finish the work, A require $$21$$ days.Hence, A alone can finish the work in $$21$$ days.Mathematics

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