A 12-hectare field is reaped by 1man, 2 women and 3 children together in 24 days. If working capabilities of a man, a woman and a child are in the ratio 7 : 4 : 2, then a 14 hectare field will be reaped by 2 men, 1 women and 5 children in:
Answer & explanation
Correct answer: option 2
Efficiency ratio : M : W : C = 7 : 4 : 3
Total efficiency of the 1st group = (1 × 7) + (2 × 4) + (3 × 2) = 21
Total efficiency of the 2nd group = (2 × 7) + (1 × 4) + (5 × 2) = 28
⇒ Efficiency × Days = Total work
⇒ \(\frac{E_1\;×\;D_1}{E_2\;×\;D_2}\) = \(\frac{W_1}{W_2}\)
⇒ \(\frac{21\;×\;24}{28\;×\;D_2}\) = \(\frac{12}{14}\)
⇒ D2 = 21