P and Q can do a work in 12 days. Q and R can do the same work in 16 days and R and P can do it in 24 days. Find the approximate time in which P, Q and R can finish the work together.
P and Q can do a work in 12 days. Q and R can do the same work in 16 days and R and P can do it in 24 days. Find the approximate time in which P, Q and R can finish the work together.
1). 11 days
2). 8 days
3). 23 days
4). 21 days
1 answers
Since, P and Q take 12 days to complete the total amount of work.
∴ In 1 day the amount of work completed by P and Q would be = 1/12
Similarly, Q and R take 16 days to complete the total amount of work.
∴ In 1 day the amount of work completed by P and Q would be = 1/16
Since, R and P take 24 days to complete the total amount of work.
∴ In 1 day the amount of work completed by P and Q would be = 1/24
Let’s assume the individual efficiencyof P, Q and R to complete the work in 1 day is p, q and r respectively.
⇒ 2(p + q + r) = $(\frac{1}{{12}} + \frac{1}{{16}} + \frac{1}{{24}} = \frac{9}{{48}} = \frac{3}{{16}})$
⇒ p + q + r = 3/32
∴ Total no. of days required = 32/3 days. = 10.66 = 11 days (approximate.)