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The ratio of the number of cows to the number of buffaloes in a farm of 600 animals is 5 : 7. When some more buffaloes join the farm the ratio of the number of cows to the number of buffaloes changes to 5 : 8. How many more buffaloes join the farm?

The ratio of the number of cows to the number of buffaloes in a farm of 600 animals is 5 : 7. When some more buffaloes join the farm the ratio of the number of cows to the number of buffaloes changes to 5 : 8. How many more buffaloes join the farm? Correct Answer 50

Given:

Number of animals in a farm = 600

Initial ratio of cow and buffalo = 5 : 7

Formula used:

If the ratio of cow and buffalo is a : b then,

Number of cow = (a/a + b) × total animals

Number of buffalo = (b/a + b) × total animals

Calculation:

Number of cows = (5/12) × 600 = 250

Number of buffaloes = (7/12) × 600 = 350

Let the number of buffaloes that join the farm be x.

According to question:

250/(350 + x) = 5/8

⇒ 2000 = 1750 × 5x

⇒ 5x = 250

⇒ x = 50

∴ 50 more buffaloes join the farm

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