Question

8. 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 1

$ANSWER</h3><h3></h3><h3>Let whole work be W.</h3><h3></h3><h3></h3><h3>⇒ Work done by A in one day =16W</h3><h3></h3><h3></h3><h3>     Work is done by B in one day =12W</h3><h3></h3><h3></h3><h3>⇒ A worked for 2 days =2×16W</h3><h3></h3><h3></h3><h3>                                        =8W</h3><h3></h3><h3></h3><h3>A and B worked for x days ( let )</h3><h3></h3><h3></h3><h3>⇒8W+x(16W+12W)=W</h3><h3></h3><h3></h3><h3>⇒x×487=87</h3><h3></h3><h3></h3><h3>⇒x=6 days.</h3><h3></h3><h3></h3><h3>Hence, the answer is 6 days.</h3><h3></h3><h3>$

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Answer 2

Answer:

A's 1 day work = 1/16

B's 1 day work = 1/12

(As A worked for 2 days alone we'll find work done by A in 2 days by multiplying his one day work by 2)

A's 2 day work = 2x(1/16) =1/8

Remaining work = 1–1/8 =7/8

( Total work is always presumed to be 1 in all such cases )

Now this remaining work will be done by A and B together .

(A+B)'s 1 day work = (1/16) + (1/12) = 7/48

A and B together can do the remaining work in = (7/8)÷(7/48) = 6 days

Total time taken = 6+2 = 8 days ANS