d P and Q can complete a work in 15 days

# Basic Math MCQ 12 (Work and days)

MCQ 12:  P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in__________days.

a) 12               b) 15                  c) 22                d) 20

Solution:

Let the amount of wok = x

For P

work in 15 days = x

so, work in 1 day =x/15

hence we simply write

Wp = x/15

Similarly for Q

Wq= x/10

Worl done by both P & Q in one day together = x/15+x/10= 5x/30= x/6

or

simply

Wp+Wq = x/6

so, Work done in two days = ​$$2\times \frac{x}{6} =\frac{x}{3}$$

So, Remaining work = ​$$x -\frac{x}{3}=\frac{2x}{3}$$

So, this remaining work is to be done by P alone!

Hence we arrange data for P as under;

 Work Days x 15 2x/3 Z

Here it is direct proportion in work and days i-e more wok more days , so

$\frac{\frac{2x}{3}}{x}=\frac{z}{15}$

hence $\frac{2}{3}=\frac{z}{15}$

hence $z= \frac {2\times15}{3}=10$

So the remaining work will be done by P in 10 days

so, total days in which work was done by P = work done with Q + work done as alone = 2+10 = 12 days!

Hence option  a is correct!

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