Question : A can do work in 18 days and B in 24 days. If they work on it together for 5 days, then find the fraction of the work that is left.
Option 1: $\frac{35}{72}$
Option 2: $\frac{7}{72}$
Option 3: $\frac{37}{72}$
Option 4: $\frac{33}{72}$
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Correct Answer: $\frac{37}{72}$
Solution :
Given: A can do a work in 18 days and B in 24 days.
Efficiency of A = $\frac{1}{18}$
Efficiency of B = $\frac{1}{24}$
Combined efficiency of A and B = $\frac{1}{18}+\frac{1}{24}$ = $\frac{7}{72}$
Hence, total work done in 5 days = $5\times \frac{7}{72}=\frac{35}{72}$
Fraction of work remaining = $1-\frac{35}{72}$ = $\frac{37}{72}$
Hence, the correct answer is $\frac{37}{72}$.
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