Question

Two numbers are such that the ratio between them is 5:2. If each is increased by 1 the ratio between the new number so formed is 7:3.Find the oringinal number

Answer 1

Assume the two numbers are x and y

x : y = 5 : 2
x/y = 5/2
x = (5y)/2

(x + 1)/(y + 1) = 7/3
3(x + 1) = 7(y + 1)
3x + 3 = 7y + 7
3(5y/2) + 3 = 7y + 7
15y/2 + 3 = 7y + 7
15y/2 - 7y = 7 - 3
15y/2 - 14y/2 = 4
y/2 = 4
y = 4 × 2
y = 8

x = (5y)/2
x = (5 × 8)/2
x = 40/2
x = 20

The original numbers are 20 and 8