P and Q can harvest a field in 5 and 7 days respectively after P has worked for 3 days, - Maths - Direct and Inverse Proportions

Question

P and Q can harvest a field in 5 and 7 days respectively after P
has worked for 3 days, he is joined by Q in how many more days will
the work be completed?

Manmeet Singh · Accepted Answer

P`s one day work = $\frac{1}{5}$

Q`s one day work = $\frac{1}{7}$

Since P worked alone for 3 days,

work completed by P = $3 \times \frac{1}{5} = \frac{3}{5}$

Work left = $1 - \frac{3}{5} = \frac{2}{5}$

Now, Q also joined P.

So, work done by them in one day = P`s one day work + Q`s one day work

= $\frac{1}{5} + \frac{1}{7} = \frac{12}{35}$

So, $\frac{12}{35}$ of work is completed in 1 day

so, $\frac{2}{5}$ of work will be completed in $\frac{35}{12} \times \frac{2}{5} = \frac{7}{6} = 1.16 d a y s$

Hence, the work will be completed on the second day when they start working together.

P and Q can harvest a field in 5 and 7 days respectively.after P has worked for 3 days, he is joined by Q.in how many more days will the work be completed?