Question : A can do a task in 8 days, while B can do it in 18 days. In how many days will the work be completed if they both work on alternate days, starting with B?
Option 1: $11 \frac{1}{3}$ days
Option 2: $12 \frac{1}{3}$ days
Option 3: $10$ days
Option 4: $10 \frac{1}{3}$ days
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Correct Answer: $11 \frac{1}{3}$ days
Solution :
Given: A can do a task in $8$ days.
B can do it in $18$ days.
Let the total work be the LCM of $(8, 18)$ i.e. $72$ units.
⇒ Efficiency of A $=\frac{72}{8} = 9$ units
⇒ Efficiency of B $=\frac{72}{18} = 4$ units
Work done by A and B in $2$ days $=(9 + 4) = 13$ units
Work done by A and B in 10 days when they work on alternate days $= 5 \times 13 = 65$ units
Remaining work $= 72 -65 = 7$ units
B's work on the $11$
th
day is $4$ units.
So, remaining work $= 7 -4 =3$ units
Time taken by A to complete $3$ units $=\frac{3}{9}=\frac{1}{3}$
Total time taken by A and B to complete the work $= 10 + 1 + \frac{1}{3}=11\frac{1}{3}$ days
Hence, the correct answer is $11\frac{1}{3}$ days.
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