4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 8 men and 6 women take to do the same job?

Correct option is B

Given:

- 4 men and 3 women finish a job in 6 days

- 5 men and 7 women finish the same job in 4 days

- We need to find the time taken by 8 men and 6 women to complete the same job

Formula Used:

- Work = Men × Days (if units of work are constant)

- Let 1 man's 1-day work = M, and 1 woman's 1-day work = W

- Total work from both groups can be equated to form equations

Solution:

Let 1 man's 1-day work = M and 1 woman's 1-day work = W

From 1st case: (4M + 3W) × 6 = 1 job => 24M + 18W = 1 …(i)

From 2nd case: (5M + 7W) × 4 = 1 job => 20M + 28W = 1 …(ii)

Multiply (i) by 5 and (ii) by 6 to eliminate M:

Equation (i) × 5: 120M + 90W = 5

Equation (ii) × 6: 120M + 168W = 6

Subtract: (120M + 168W) − (120M + 90W) = 6 − 5

=> 78W = 1 => W = $$\frac{1}{78}$$​​

Substitute W in (i): 24M + 18 × ($$\frac{1}{78}$$​) = 1

​$$\Rightarrow 24M + \frac{18}{78} = 1 \\\ \\\Rightarrow 24M = 1 - \frac{18}{78} = \frac{60}{78} \\\ \\\Rightarrow M = \frac{60}{1872} = \frac{5}{156}$$​​

Now, 8 men and 6 women one-day work = $$8 \times \frac{5}{156} + 6 \times \frac{1}{78} = \frac{40}{156} + \frac{6}{78} = \frac{40}{156} + \frac{12}{156} = \frac{52}{156} = \frac{1}{3}$$​​

So, Time = $$\frac{1 }{ \frac{1}{3}}$$​ = 3 days

Exam Trick: ​