2 men and 3 women can earn ₹49 in 7 days. 3 men and 6 women can earn ₹96 in 8 days. In what time 1 man and 1 woman earn ₹27?

Correct option is A

Given:

2 men + 3 women earn ₹49 in 7 days.

3 men + 6 women earn ₹96 in 8 days.

Find the time for 1 man + 1 woman to earn ₹27.

Formula Used:

$$\text{Time} = \frac{\text{Total earnings}}{\text{Combined daily earnings}}$$​​

Solution:

(2 men + 3 women) daily earnings =$$\frac{₹49}{ 7 }$$​days = ₹7

(3 men + 6 women) daily earnings = $$\frac{₹96 }{ 8 \text{days}} = ₹12$$​​

Let 'm' be the daily earnings of 1 man and 'w' be the daily earnings of 1 woman.

2m + 3w = 7 ...(1)

3m + 6w = 12 ...(2)

Multiply equation (1) by 2: 4m + 6w = 14 ...(3)

Subtract equation (2) from equation (3): (4m + 6w) - (3m + 6w) = 14 - 12

m = 2

Substitute m = 2 in equation (1): 2(2) + 3w = 7

4 + 3w = 7

3w = 3

w = 1

Combined daily earnings of 1 man and 1 woman:

m + w = 2 + 1 = ₹3

Time to earn ₹27:

​$$\text{Time} = \frac{\text{Total earnings}}{\text{Combined daily earnings}}$$​​

Time $$= \frac{₹27 }{ ₹3}$$​per day = 9 days.