Question : D alone can do a work in 20 days and E alone can do the same work in 25 days. If they work on it together for 8 days. then the fraction of the work that is left is:
Option 1: $\frac{11}{25}$
Option 2: $\frac{7}{25}$
Option 3: $\frac{9}{100}$
Option 4: $\frac{51}{100}$
Correct Answer: $\frac{7}{25}$
Solution :
D alone can do a work in 20 days and E alone can do the same work in 25 days.
D's 1 day's work = $\frac{1}{20}$
E's 1 day's work = $\frac{1}{25}$
(D + E)'s 1 day's work = $\frac{1}{20}+\frac{1}{25}=\frac{9}{100}$
(D + E)'s 8 days work = $\frac{9}{100}×8=\frac{18}{25}$
Work left after 8 days = $1-\frac{18}{25}=\frac{7}{25}$
Hence, the correct answer is $\frac{7}{25}$.
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