Question

Palone can do 1/2 of a work in 6 days and Q alone can do 2/3
of the same work in 4 days.
In how many days working together, will they finish 3/4 of the work?​

Answer 1

Step-by-step explanation:

3 days is the best answer

Answer 2

P and Q will together finish 3/4th of the work in 3 days, if 1/2 work is done by P in 6 days and 2/3rd of the work is done in 4 days.

Step-by-step explanation:

P alone can do  $\frac{1}{2}$  of the work in 6 days

So, P can do the whole work in = $\frac{6}{\frac{1}{2}}$ = 6 * 2 = 12 days

Q alone can do $\frac{2}{3}$ of the same work in 4 days

So, Q can do the whole work in = $\frac{4}{\frac{2}{3}}$ = $4 * \frac{3}{2}$ = 6 days

Now,

Work done by P in 1 day = $\frac{1}{12}$

Work done by Q in 1 day = $\frac{1}{6}$

∴ Work done by P and Q together in 1 day is given by,

= $\frac{1}{12} + \frac{1}{6}$

= $\frac{1 + 2}{12}$

= $\frac{3}{12}$

= $\frac{1}{4}$

If, 1 whole work is done by P and Q together in 4 days

Then, $\frac{3}{4}$th of the work will be done in = 4 * $\frac{3}{4}$ = 3 days

Thus, P and Q will together finish the 3/4 th of the work in 3 days.

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