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Standard VIII

Mathematics

Transposing Method

'A' can do a ...

Question

'A' can do a piece of work in 14 days while 'B' can do it in 14 days. They begin together. But, 3 days before the completion of work, 'A' leaves off.
Find the total number of days taken to complete the work.

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Solution

We will solve this using the LCM technique.

A takes 14 Days & B takes 21 Days. So, let the total work be LCM(14,21) = 42 Units

A -> 14 days = 3 Units/day
B -> 21 days = 2 Units/day
A + B = 5 Units/day

Now, for the last 3 days , only B worked as A left.

So, work done in the last three days = 2×3= 6 units

Work done by A & B together = 42–6 = 36 units

Time taken = 36/5 = 7.2 days

Thus, TOTAL TIME = 3+7.2 = 10.2 Days

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