The number of hens, ducks and goats in farm P are 65, 91 and 169, respectively. All the hens, ducks and goats are sent from farm P to farm Q. The number of hens, ducks and goats in farm Q before this transfer were in the ratio 5 : 14 : 13. After the transfer, the new ratio of hens : ducks : goats in farm Q becomes 5 : 14 : 13. All the hens, ducks and goats are sent from farm P to farm Q. The new ratio of hens, ducks and goats in farm Q is A. 5 : 7 : 13 B. 5 : 14 : 13 C. 10 : 21 : 26 D. 21 : 39 : 26

GATE 2021 · General Aptitude · Ratio Proportion · medium

Answer: The new ratio of hens : ducks : goats in farm Q is 10 : 21 : 26. Answer: C.

  1. Find Farm Q's initial animal counts: From P: 65 = 5*13, 91 = 7*13, 169 = 13*13. Notice 65 = 5*13 matches 5m with m=13. So Q initially has 5*13=65 hens, 14*13=182 ducks, 13*13=169 goats.
  2. Add Farm P animals to Farm Q: Hens: 65 + 65 = 130. Ducks: 182 + 91 = 273. Goats: 169 + 169 = 338.
  3. Simplify the ratio 130 : 273 : 338: 130 = 2*5*13, 273 = 3*7*13, 338 = 2*13^2. GCD = 13. So 130/13 : 273/13 : 338/13 = 10 : 21 : 26.