Question : A can complete $\frac{1}{3}$rd of a task in 7 days and B can complete $\frac{2}{7}$th of the same task in 10 days. In how many days can A and B together complete the task?
Option 1: $12 \frac{3}{8}$
Option 2: $11 \frac{7}{8}$
Option 3: $13 \frac{1}{8}$
Option 4: $15 \frac{1}{7}$
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Correct Answer: $13 \frac{1}{8}$
Solution :
Given: A can do $\frac{1}{3}$rd of a task in 7 days.
Total work done = Number of days × Efficiency
So, A can complete the task in $(7 × 3) = 21$ days
B can do $\frac{2}{7}$th of the same task in $10$ days.
So, B can complete the task in $(10 × \frac{7}{2}) = 35$ days
Total work is the LCM of $(21, 35) = 105$ units
Efficiency of A is $\frac{105}{21} = 5$
Efficiency of B is $\frac{105}{35} = 3$
$\therefore$ A and B together will complete the task in $\frac{105}{5+3}=\frac{105}{8} =13 \frac{1}{8}$ days
Hence, the correct answer is $13 \frac{1}{8}$ days.
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