Question

8 men and 2 women together can finish a piece of work in 24 days. In how much time will 40 men and 45 women together complete 1.5 times the work, if the work done by 16 men in 8 hours is equal to the work done by 2 women in 24 hours?
1. 9 days
2. 3 days
3. 6 days
4. 10 days

Answer 1

Correct Answer - Option 2 : 3 days

Given: 

8 men and 2 women can do a piece of work in 24 days

16 men in 8 hours is equal to the work done by 2 women in 24 hours

Formula:

Total work = Efficiency × Time Taken

Calculation:

Let efficiency of 1 man and 1 woman be M and W respectively

According to the question,

(8M + 2W) × 24 = Total work      ----(1)

Now, 

16M × 8 = 2W × 24

⇒ 8M = 3W      

Putting the value of 8M = 3W in equation (1),

(8M + 2W) × 24 = Total work 

⇒ (3W + 2W) × 24 = 120 W

Then,

8M = 3W

⇒ (8M) × 5 = (3W) × 5(Multiplying both sides with 5)

⇒ 40M = 15W

Again, According to the question,

(40M + 45W) × d = 120W × 1.5

⇒ (15W + 45W) × d = 120W × 1.5

⇒ 60W × d = 120W × 1.5

⇒ d = 3 days

∴ The required time will be 3 days.