Tamil Nadu Board of Secondary EducationSSLC (English Medium) (5 to 8) Class 8

# 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? - Mathematics

Sum

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?

#### Solution

P can do a piece of work in 12 days.

∴ P’s 1 day work = 1/12

P’s 3 day’s work = 3 xx 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 = 1/2 + 1/15

= 5/60 + 4/60

= 9/60

∴ Number of days required to finish the remaining work 9

= "Remaining work"/(("P" + "Q")"'s"  1  "day work")

= (9/12)/(9/60)

= 9/12 xx 60/9

= 5

Remaining work lasts for 5 days

Total work lasts for 3 + 5 = 8 days.

Concept: Time and Work
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Chapter 4: Life Mathematics - Exercise 4.5 [Page 152]