Question

In a plantation, the ratio of the number of apple trees to the number of mango trees was 6 : 11. A fire destroyed 78 of the apple trees and the ratio of apple trees to the number of mango trees became 1 : 4. How many trees were left in the plantation after the fire?

Answer 1

a/m = 6/11 so m = 11 a / 6
(a-78) / m = 1/4 so m = 4 a - 312

4 a - 312 = 11 a/6
312 = 4 a - 11 a / 6
312 = (24 - 11) a/6 = 13 a/6
a = 144
m = 11 a /6 = 264
so after fire
n = 264 + 144 - 78 = 330

Answer 2

or
number of apple trees = 6x
number of mango trees = 11x

(6x-78) : 11x = 1 : 4
24x - 312 = 11x
13x = 312
x = 24
trees left = 6x + 11x - 78 = 144+264-78 = 330