25 men and 45 women can complete a piece of work in 15 days, while 15 men and 60 women can complete it in 20 days. In how many days can 69 men and 67 women complete the work?

Given:

25 men and 45 women complete work in 15 days

15 men and 60 woman complete the work in 20 days

Formula Used:

M₁D₁ = M₂D₂

Calculations:

As in both case they complete the same work 

so,

⇒ M1D1 = M2D2

⇒ \((25M + 45W) \times 15 = (15M+60W)\times 20\)

⇒ \((25M + 45W) \times 3 = (15M+60W)\times 4\)

⇒ 75M + 135W = 60M + 240W

⇒ 75M - 60M = 240W -135W

⇒ 15M = 105W

⇒ \(\frac{M}{W}=\frac{105}{15}\)

⇒ \(\frac{M}{W}=\frac{7}{1}\)

⇒ Efficiency of Men = 7

⇒ Efficiency of Woman = 1

⇒ Total efficiency of men and woman = 25M + 45W = 25 × 7 + 45 × 1  = 175 + 45 = 220

⇒ Total work = Efficiency × Time = 220 × 15 = 3300

Now, the Efficiency of 69 men and 67 women

⇒ Efficiency = 69 × 7 + 67 × 1 = 483 + 67 = 550

Time is taken by 69 men and 67 women to complete the work

⇒ Time = Total work / Efficiency = 3300 / 550 = 6 days

⇒ Hence, The time taken by 69 men and 67 women is 6 days