Correct Answer - Option 1 : 27

Let efficiency of 1 man, 1 woman and 1 boy be x, y and z respectively.

According to the question

18x × 64 = 9y × 108 = 7z × 216

⇒ 32x = 27y = 42z

Let 32x = 27y = 42z = k, then

⇒ 32x = k

⇒ x = k/32

Similarly,

⇒ y = k/27 and z = k/42

⇒ Ratio of x : y : z = k/32 : k/27 : k/42 = 6048k/32 : 6048k/27 : 6048k/42 = 189 : 224 : 144

⇒ Total work = 18 × 189 × 64

⇒ Total efficiency of 16 men, 9 women and 21 boys in 1 day = 16 × 189 + 9 × 224 + 144 × 21 = 3024 + 2016 + 3024 = 8064

∴ The work will be complete in (18 × 189 × 64)/8064 = 27 days