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Atul does half as much work as Anshu in $\dfrac 4 5$ of the time. If together they take $16$ days to complete the work, how many days shall Anshu take to do it?

1. 23
2. 25
3. 26
4. 30
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0

Let speed of Anshu be $a$.

Time Anshu takes for $x$ amount of work $= \frac{x}{a}$.

Time Atul takes for $x$ amount of work $=2 \times \frac{4x}{5a} = \frac{8x}{5a}$.

Speed of Atul $=\frac{5a}{8}$

When both works, effective speed $= a + \frac{5a}{8} = \frac{13a}{8}$.

16 days to complete work with speed $\frac {13a}{8}$.

So, no. of days to complete with speed $a = 16 \times \frac{13a}{8}\times \frac{1}{a} = 26.$
by Veteran (422k points)
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-->  Let Anshu takes x Days  ,  than Atul takes (2*(4/5)x) = 8x/5 Days.

--> Together Atul and Anshu takes = 16 Days . So, Together 1 Day work = 1 / 16 .

--> Taking 1(one) Day work of , Anshu + Atul = Together .

--> (1 / x) + (5 / 8x) = 1 / 16  , Solving x = (16*13) / 8 = 26 Days [Anshu].

by Active (2.4k points)