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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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some one try this please

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 (434k points)
selected

-->  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)

This method can be used for solve the question quickly . As mention in the question there are two men Atual and Anshu. And work to done by individual or together should be same. So let us assume Anshu time taken is x days so Atual time taken will be (2* 4x/5)=8x/5

Now Solution

Men         Atual                           Anshu                      Atual+ Anshu

Rate        W/T = 1  (R1)           W/T = 8/5 (R2)          R1+R2 = 13/5

Time        8x/5                            x                                16(Given in Question)

Work       8x/5                            8x/5                               208/5

Take Lcm of Atual and Anshu and put in work done it will come 8x/5. Now Calculate the Rate of Each . Then Add the Rate for together. Now together 13/5 . Calculate the Together work done which will come 208/5. As Work done to be done should be equal by individual and together. So Now we can say Anshu Work done should be equal to 208/5 i.e 8x/5 should be equal to 208/5. So 8x/5 = 208/5  . Upon evaluating the x it will give 26 which is Anshu time period . Ans . Let me know for any Confession,

by (17 points)

$\text{Total work} =\text{Efficiency (or) One day work}\times \text{Total time}$

$\textbf{W = DMTE}$

D = Number of days

M = Number of men

T = Number of hours per day

E = Efficiency

W = Amount of work

Now, $D_{1}M_{1} = D_{2}M_{2}$

$\implies \dfrac{\frac{4}{5}\times M_{1}}{\frac{1}{2} W} = \dfrac{1 \times M_{2}}{W}$

$\implies 8M_{1} = 5 M_{2}$

$\implies M_{1} = \dfrac{5}{8}M_{2}$

again, $x \times M_{2} = 16 \times (M_{1} + M_{2})$

$\implies x \times M_{2} = 16 \times \bigg(\dfrac{5}{8}M_{2} + M_{2}\bigg)$

$\implies x \times M_{2} = 16 \times \dfrac{13}{8}M_{2}$

$\therefore x = 26$ days

by Veteran (60.8k points)