Question

A farmer planted only apples and pears on his orchard. There are 120 more pears than apples. 1/4 of the apples and 2/13 of the pears were rotten. If 1/5 of the fruits were rotten, how many fruits are there in the orchard?

Answer 1

p = a + 120
a/4 rotten
2p/13 rotten

a/4 + 2p/13 = 1/5 ( p+a ) or a/4-a/5 = p/5 - 2p/13
a/20 = 13 p / 65 - 10p/65 = 3 p/65
65 a/20 = 3 p
65 a = 60 p
p = 13 a /12
and we know
p = a + 120
a +120 = 13 a/12
12 a/12 + 120 = 13 a/12
a/12 = 120
a = 1440
p = 1560
sum = 3000