Question : 30 women working 5 hours a day can complete a work in 18 days, In how many days will 21 women working 8 hours a day complete the same work?
Option 1: $18 \frac{7}{13}$ days
Option 2: $17 \frac{11}{13}$ days
Option 3: $16 \frac{1}{14}$ days
Option 4: $13 \frac{3}{14}$ days
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Correct Answer: $16 \frac{1}{14}$ days
Solution :
One hour work by 30 women = $\frac{1}{(18 × 5)}$
⇒ One hour work by 30 women = $\frac{1}{90}$
⇒ One hour work by 1 woman = $\frac{1}{90 × 30}$
⇒ One hour work by 1 woman = $\frac{1}{2700}$
⇒ One hour work by 21 women = $\frac{21}{2700}$
⇒ 8 hour work by 21 women in 1 day = $\frac{21× 8}{2700}$
⇒ 8 hour work by 21 women in 1 day = $\frac{14}{225}$
Then the whole work will be done by 21 women in $\frac{225}{14}$ days
Working 8 hrs a day 21 women can complete the work in = $16\frac{1}{14}$ days
Hence, the correct answer is $16\frac{1}{14}$ days.
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