Correct Answer: 6

Solution : According to the question, they complete the same work
⇒ M ₁ D ₁ = M ₂ D ₂
⇒ (25M + 45W) × 15 = (15M + 60W) × 20
⇒ (25M + 45W) × 3 = (15M + 60W) × 4
⇒ 75M + 135W = 60M + 240W
⇒ 75M – 60M = 240W – 135W
⇒ 15M = 105W
⇒ $\frac{\text{M}}{\text{W}}=\frac{7}{1}$
Let the efficiency of Men = 7 and the efficiency of Women = 1
⇒ Total efficiency of 25 men and 45 women = 25M + 45W = 25 × 7 + 45 × 1 = 175 + 45 = 220
Now, Total work = Efficiency × Time = 220 × 15 = 3300
And, The Efficiency of 69 men and 67 women
⇒ 69 × 7 + 67 × 1 = 483 + 67 = 550
$\therefore$ The time is taken by 69 men and 67 women to complete the work = $\frac{\text{Total work}}{\text{Efficiency}} = \frac{3300}{550} = 6$ days
Hence, the correct answer is 6.