Question : 15 men complete a work in 10 days. 15 women complete the same work in 12 days. If all these men and women work together, then the number of days required to complete that work is:
Option 1: $5\frac{5}{11}$
Option 2: $4\frac{3}{11}$
Option 3: $7\frac{2}{11}$
Option 4: $6\frac{4}{11}$
Correct Answer: $5\frac{5}{11}$
Solution :
Time taken by 15 men to complete the work = 10 days
⇒ Part of work done by 15 men in a day = $\frac{1}{10}$
Time taken by 15 women to complete the work = 12 days
⇒ Part of work done by 15 women in a day = $\frac{1}{12}$
Let time taken by (15 men + 15 women) to complete the work = $x$ days
⇒ Part of work done by (15 men + 15 women) in a day = $\frac{1}{x}$
⇒ $\frac{1}{10}$ + $\frac{1}{12}$ = $\frac{1}{x}$
⇒ $\frac{1}{x}$ = $\frac{11}{60}$
Time taken by (15 men + 15 women) to complete the work = $\frac{60}{11}$ = $5\frac{5}{11}$days
Hence, the correct answer is $5 \frac{5}{11}$.
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