A and B can complete a piece of work in 12 and 18 days

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RRB ASM Exam (Ajmer) 2007 click here to view all questions

A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in

A

B

C

D

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Answer is: $14\frac{1}{3}days$ Explanation: A can complete total work in 12 days One day work of A = $\frac{1}{2}$part B can complete work in 18 days One day work of B = $\frac{1}{18}$part A and B together can complete work in one day, =$\frac{1}{12}+\frac{1}{18}$ =$\frac{18+12}{216}$=$\frac{30}{216}$=$\frac{15}{108}$ =$\frac{5}{36}$part Evidently, the work done by A and B during 7 pairs (14 days) =$7\times \frac{5}{36}=\frac{35}{36}$ Remaining work = $(1-\frac{35}{36})=\frac{1}{36}$ Now, on 15th  day it is  A's turn. Now $\frac{1}{12}$work is done by A in 1 day. $\frac{1}{36}$ work will be done by A in $[12\times \frac{1}{36}]=\frac{1}{3}$ day So, total time taken = $14\frac{1}{3}$ days Nithin K ? answered Nov 23 '2016 at 21:4 All Comments

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