How much has Tanay scored in History?

Question

In a class test Tanay scored 160 marks in Geography and History together. If one third of his marks in Geography equals to half of the marks he scored in History, then how much has he scored in History?

Answer 1

64

Let the marks in Geography be G and History be H.
Eq 1: G + H = 160
Eq 2: G/3 = H/2
By the problem:
G = 160 - H

Therefore, putting the value of G in Eq 2:
(160 - H)/3 = H/2
or, 320 - 2H = 3H
or, 3H + 2H = 320
or, 5H = 320
or, H = 64

Answer 2

Of every 3 points in Geo, he scored 2 points in History.
160 / 5 * 2 = 64 points in History.