A38 days
B32 days
C40 days
D35 days
Answer:
C. 40 days
Read Explanation:
Solution:
Given:
12 men (M) can do the work in 54 days
20 women (W) can do the same work in 54 days
Concept used:
If n person can do the work in x days then 1 person can do the same work in nx days
If a person completes work in m days then the person will complete 1/m work in one day.
Calculation:
12 men can do the work in 54 days
⇒ 1 man can do the work in 12 × 54 = 648 days
⇒ 9 men can do the work in 648/9 = 72 days
⇒ 9 men can do 1/72 of work in 1 day
20 women can do the work in 54 days
⇒ 1 woman can do the work in 54 × 20 = 1080 days
⇒ 12 women can do the work in 1080/12 = 90 days
⇒ 12 women can do 1/90 of work in 1 day
⇒ 9 men and 12 women can do 1/72 + 1/90 work in a day
⇒ 9 men and 12 women can do (5 + 4)/90 work in a day
⇒ 9 men and 12 women can do 1/40 of work in 1 day
⇒ 9 men and 12 women can do 1 work in 1 × 40 days
∴ 9 men and 12 women can do 1 work in 40 days.
Alternate:
12 men can do the work in 54 days
⇒ 1 man can do the work in 12 × 54 = 648 days
⇒ 9 men can do the work in 648/9 = 72 days
20 women can do the work in 54 days
⇒ 1 woman can do the work in 54 × 20 = 1080 days
⇒ 12 women can do the work in 1080/12 = 90 days
⇒ 9 men and 12 women can do work in 360/(5+4)
⇒ 9 men and 12 women can do work in 360/9
∴ 9 men and 12 women can do work in 40 days.
Short Cut:
Formula used:
M1 × T1 = M2 × T2
Where M is men and T is time
Calculation:
12M × 54 = 20W × 54
⇒ M/W = 5/3 or M = 5 and W = 3
Total work = No of Women × Efficiency × Days
20 × 3 × 54 = 3240
9M + 12W = 9 × 5 + 12 × 3 = 81
Time = 3240/81 = 40 days
∴ 9 men and 12 women can do work in 40 days.