Question

P and q need 8 days to complete a work. q and r need 12 days to complete the same work. but p, q and r together can finish it in 6 days. how many days will be needed if p and r together do it

Answer 1

heyate hope it helps

Answer 2

Answer:

p and r together can complete the work in 8 days.

Step-by-step explanation:

We have been given that P and q need 8 days to complete a work. It means that  p and q's, 1 day's work is given by

$\frac{1}{p}+\frac{1}{q}=\frac{1}{8}......(1)$

Similarly, for q and r

$\frac{1}{q}+\frac{1}{r}=\frac{1}{12}......(2)$

And for p,q and r

$\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=\frac{1}{6}......(3)$

Plugging the value of equation 2 in equation 3, we get

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

Subtract 1 and 2, we get

$\frac{1}{p}-\frac{1}{r}=\frac{1}{8}-\frac{1}{12}\\\\\frac{1}{p}-\frac{1}{r}=\frac{1}{24}\\\\\frac{1}{12}-\frac{1}{r}=\frac{1}{24}\\\\\frac{1}{r}=\frac{1}{24}$

Now, let us find

$\frac{1}{p}+\frac{1}{r}=\frac{1}{12}+\frac{1}{24}\\\\=\frac{3}{24}\\\\=\frac{1}{8}$

Hence, p and r together can complete the work in 8 days.