P and Q can do a piece of work in 12 days and 15 days respectively. P

1.	P and Q can do a piece of work in 12 days and 15 days respectively. P started the work alone and then, after 3 days Q joined him till the work was completed. How long did the work last?
Answer» p can do a piece of work in 12 days. ∴ p’s 1 day work = 1/12 p’s 1 day work = 3 × 1/12 = 3/12 Q can do a piece of work in 15 days. ∴ Q’s 1 day work = 1/15 Remaining work after 3 days = 1 – 3/12 = 9/12 (P + Q)’s 1 day work = 1/12 + 1/15 = 5/60 + 4/60 = 9/60 Number of days required to finish the remaining work = Remaining work/(P+Q)′s 1 day work = 9/12/9/60 = 9/12 × 60/9 = 5 Remaining work lasts for 5 days. Total work lasts for 3 + 5 = 8 days.

P and Q can do a piece of work in 12 days and 15 days respectively. P started the work alone and then, after 3 days Q joined him till the work was completed. How long did the work last?

Answer»

p can do a piece of work in 12 days.

∴ p’s 1 day work = 1/12

p’s 1 day work = 3 × 1/12 = 3/12

Q can do a piece of work in 15 days.

∴ Q’s 1 day work = 1/15

Remaining work after 3 days = 1 – 3/12 = 9/12

(P + Q)’s 1 day work

= 1/12 + 1/15 = 5/60 + 4/60 = 9/60

Number of days required to finish the remaining work

= Remaining work/(P+Q)′s 1 day work

= 9/12/9/60 = 9/12 × 60/9 = 5

Remaining work lasts for 5 days. Total work lasts for 3 + 5 = 8 days.