Question

P , q and r together can complete a work in 20 days. P alone can complete the work in 40 days, q alone in 60 days then in how many daya r alone can complete the work

Answer 1

Step-by-step explanation:

Given:

p , q and r together can complete a work in 20 days.

Therefore,

One day's work of p, q and r:

$\frac{1}{p} +\frac{1}{q}+\frac{1}{r}=\frac{1}{20}....(1)$

Since, P alone can complete the work in 4.

Therefore,

One day's work of p:

$\frac{1}{p} =\frac{1}{40}....(2)$

Since, q alone can complete the work in 4.

Therefore,

One day's work of q:

$\frac{1}{q} =\frac{1}{60}....(3)$

From equations (1), (2) & (3) we have:

$\frac{1}{40} +\frac{1}{60}+\frac{1}{r}=\frac{1}{20}....(1)\\</p><p>\frac{1}{r}= \frac{1}{20}-\frac{1}{40} - \frac{1}{60}\\</p><p>\frac{1}{r}= \frac{6}{120}-\frac{3}{120} - \frac{2}{120}\\</p><p>\frac{1}{r}= \frac{6-3-2}{120}\\</p><p>\frac{1}{r}= \frac{6-5}{120}\\</p><p>\frac{1}{r}= \frac{1}{120}\\</p><p>\implies r = 120$

Hence, r alone can complete the work in 120 days.