Question

P alone 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 daysworking together will they finish 3/4 of the work?

Answer 1

Answer:

For P

in 6 days 1/2 unit

in 1 day 1/12 unit

For Q

in 4 days 2/3 unit

in 1 day 2/4*3= 1/6 unit

Both in 1 day 1/12+ 1/6 = 1/4 unit

now 1/4 in 1 day

so, 3/4 in 3 days.

Answer 2

In 3 days working together they will finish 3/4 of the work.

Step-by-step explanation:

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

P alone can do total work in =  $\frac{1}{2}$ ÷ 6

                                                = 12 days

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

Q alone can do total work in =  $\frac{2}{3}$ ÷ 4

                                                = 6 days

P can do work in one day = $\frac{1}{12}$

Q can do work in one day = $\frac{1}{6}$

Together they can work in number of days  = $\frac{1}{12}+\frac{1}{6}$

                                                                        = $\frac{1+2}{12} = \frac{3}{12}$

                                                                        = $\frac{1}{4}$  = 4 days

Since one work they can do in 4 days.

They will finish working together 3/4 of the work = $\frac{3}{4}\times 4$

                                                                                  = 3 days.

In 3 days working together they will finish 3/4 of the work.

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