A man can complete a work in 20 days and a woman can complete the same work in 45 days. In how many days 2 men and 3 women can complete the same work?

Correct option is B

Given:

Time taken by 1 man to complete the work = 20 days
Time taken by 1 woman to complete the work = 45 days
Number of men = 2
Number of women = 3

Formula Used:
Work Rate = $$\frac{1 }{\text{ Time}}$$​​

Total Work Rate = (Number of men × Man’s rate) + (Number of women × Woman’s rate)

Time =$$\frac{1 }{\text{ Total Work Rate}}$$​​

Solution:
Work rate of 1 man = $$\frac{1}{20}$$​​
Work rate of 1 woman = $$\frac{1}{45}$$​​

Combined rate of 2 men and 3 women = 2 × $$\frac{1}{20}$$​ + 3 × $$\frac{1}{45}$$​​
= $$\frac{1}{10} + \frac{1}{15}$$​​

$$=\frac{3+2}{30}$$​

= $$\frac16$$​​

Time to complete the work =$$\frac{1 } {\frac16}$$​ = 6 days

Alternate Method:

Formula Used:

Efficiency $$= \frac{\text{Total Work }}{\text{ Time}}$$​​
Total Efficiency = (Men's efficiency × No. of men) + (Women's efficiency × No. of women)

Solution:
Assume total work = LCM of 20 and 45 = 180 units

Efficiency of 1 man = $$\frac{180 }{ 20}$$​ = 9 units/day
Efficiency of 1 woman = $$\frac{180 }{ 45}$$​ = 4 units/day

Total efficiency of 2 men and 3 women = (2 × 9) + (3 × 4) = 18 + 12 = 30 units/day

Time  = 180 ÷ 30 = 6 days