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Question 3 Time and Work Exercise 13A

A and B can finish a piece of work in 16 days and 12 days respectively. A

started the work and worked at it for 2 days. He was then joined by B. Find

the total time taken to finish the work.

Answer:

we know that,

Number of days A required to do a piece of work = 16days

Number of days B required to do a piece of work = 12days

∴ We can calculate, work done by A in 1 day = 1/16

Work is done by B in 1 day = 1/12

Alone works for 2 days and the work completed by A in 2 days = 2 × 1/16 = 1/8

∴ work left = 1- 1/8 = 7/8

Work done by A, B together in a one day = 1/16 + 1/12 = 7/48

∴ they can work together in 48/7 days

But 7/8th work is completed by both A and B

∴ the time required to complete 7/8th work together by A and B = 7/8 × 48/7 = 6days

Time is taken to finish the work = 6 + 2 = 8days(2 is added because 1/8 work is done by A

alone)

∴ The total time is taken to complete the work =8days.

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