Question : Akbar can complete a piece of work alone in 12 days, while Anthony can complete the same work alone in 20 days. If they work on alternate days with Anthony starting the work, then in how many days can they complete the whole work?
Option 1: $15$ days
Option 2: $16$ days
Option 3: $14 \frac{4}{5}$ days
Option 4: $15 \frac{1}{5}$ days
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Correct Answer: $15 \frac{1}{5}$ days
Solution : LCM of 12 and 20 is 60. So, Total work = 60 units Now, Efficiency of Akbar = $\frac{\text{Total unit of work}}{\text{No. of days}}=\frac{60}{12}= 5$ unit/day ⇒ Efficiency of Anthony = $\frac{\text{Total unit of work}}{\text{No. of days}}=\frac{60}{20}= 3$ unit/day ⇒ Total Efficiency = (5 + 3) = 8 unit/day Now, in 2 days = 8 units of work will be done. ⇒ In 7 pairs of days (7 × 2) = 8 × 7 = 56 unit of work will be done. Work left = 60 – 56 = 4 units ⇒ As Anthony starts the work, his efficiency is 3 units/day ⇒ On the 15 th day Anthony will do 3 more units of work i.e. ( 56 + 3) = 59 units of work is done. Now, the remaining work will be done by Akbar in = $\frac{1}{5}$th day ⇒ Total days = $(14 +1 +\frac15)$ days = $15\frac15$ days Hence, the correct answer is $15\frac15$ days.
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