4 men can complete a piece of work in 10 days, while 3 women can do it in 16 days. In how many days can 6 women and 5 men complete this work?

Correct option is C

Given:

4 men → 10 days

3 women → 16 days

Find time taken by 6 women + 5 men.

Formula Used:

Efficiency = $$\frac{1}{\text{Time}}$$​​

Solution:

Work done by 4 men in 1 day = $$\frac{1}{10}$$​​

So, work done by 1 man in 1 day = $$\frac{1}{10 \times 4} = \frac{1}{40}$$​​

Work done by 3 women in 1 day =  $$\frac{1}{16}$$​​

So, work done by 1 woman in 1 day = $$\frac{1}{16 \times 3} = \frac{1}{48}$$​​

Efficiency of 5 men = $$5 \times \frac{1}{40} = \frac{5}{40} = \frac{1}{8}$$​

Efficiency of 6 women = $$6 \times \frac{1}{48} = \frac{6}{48} = \frac{1}{8}$$​​

Total efficiency of group = $$\frac{1}{8} + \frac{1}{8} = \frac{1}{4}$$​​

Time required = $$\frac{1}{\frac{1}{4}}$$​ = 4 days

Alternate Solution (Exam Trick):