Question

X and Y can do a piece of work in 10 days and 6 days respectively they work together for 2 days and Y leaves the work. In how many days X will finish the remaining work?

Answer 1

X and Y do a piece of work in 10 days and 6 days.

So,

$\sf{Work \:done \:by \:X\: in \:one\: day\: =\: {\frac{1}{10}}}$

And

$\sf{Work \:done \:by \:Y\: in \:one\: day\: =\: {\frac{1}{6}}}$

Now,

$\sf{Work\:done\:by\:both\:X\:and\:Y\:in\:one\:day}$

$\implies\:\sf{\frac{1}{10}\:+\:\frac{1}{6}}$

$\implies\:\sf{\frac{3\:+\:5}{30}}$

$\implies\:\sf{\frac{8}{30}}$

$\implies\:\sf{\frac{4}{15}}$

Both X and Y work together for 2 days.

So,

$\sf{Work\:done\:by\:X\:and\:Y\:in\:2\:days}$

$\implies\:\sf{\frac{4}{15}\:\times\:2}$

$\implies \:\sf{\frac{8}{15}}$

$\sf{Remaining \:work\:=\:1\:-\:\frac{8}{15}}$

$\implies\:\sf{\frac{7}{15}}$

We have to find that in how many days X will complete the remaining work.

From above calculations we find that Remaining work is 7/15 and X do a piece of work in 10 days.

So,

$\bold{\underline{\sf {Time\:taken\:by\:X\:to\:complete \:the\:remaining }}}$$\bold{\underline{\sf {work}}}$

$\implies \:\sf{\frac{7}{15}\:\times\:10}$

$\implies \:\sf{\frac{14}{3}}$

X complete the remaining work in 14/3 days.

Answer 2

Answer:-

$\bold{\: \dfrac{14}{13} } \: days$

Explanation:-

Given:-

• x can do a piece of work in 10 days
• y can do a piece of work in 6 days
• Both x and y work together for 2 days and y leaves the work

To Find:-

The time taken by X to finish the work

Solution:-

Work done by X in one day = $\dfrac{1}{10}$

Work done by Y in one day= $\dfrac{1}{6}$

Given, both X and Y work together for 2 days

work done by X in 2 days = $2 \times \dfrac{1}{10}$ = $\dfrac{1}{5}$

Work done by Y in 2 days = $2 \times \dfrac{1}{6}$ = $\dfrac{1}{3}$

Work done by both X and Y in two days

${\rightarrow} \: \dfrac{1}{5}+ \dfrac{1}{3}$

${\rightarrow} \: \dfrac{3+5}{15}$

${\rightarrow} \: \dfrac{8}{15}$

Now, Y leaves the work

Work remaining :-

${\rightarrow} \: 1 - \dfrac{8}{15}$

${\rightarrow} \: \dfrac{15 - 8}{15}$

${\rightarrow} \: \dfrac{7}{15}$

Time taken by X to do the remaining work

${\rightarrow} \: \dfrac{\frac{7}{15}}{10}$

${\rightarrow} \: \dfrac{7}{15} \times 10$

$\bold{{\rightarrow} \: \dfrac{14}{13} } \: days$

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