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Question

# Grass in lawn grown equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass. How many cows are needed to eat the grass in 96 days?

A
20 cows
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B
24 cows
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C
28 cows
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D
32 cows
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Solution

## The correct option is A 20 cowsLet n,g,r, and c be the no. of cows, grass initially, the rate at which grass grow/day, and grass eaten by cow/day respectively.Now according to the question-It takes 24 days for 70 cows to eat the whole of the grass.g+24r=70×24c=1680c⟶(i)g+60r=60×30c=1800cAgain, given that it takes 60 days for 30 cows to eat the whole of the grass.∴g=1800c−60r⟶(ii)From eqn(i)&(ii), we havec=310r⟶(iii)Now, to eat the grass in 96 days-g+96r=96×nc⇒96×nc=1800c−60r+96r=1800c+36r=1800c+120c=1920c⇒n=20Hence, 20 cows are needed to eat the grass in 96 days.

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