Question

two numbers are such that the ratio between them is 3 : 4. If 16 added to both numbers the ratio between the New numbers so formed is 5 : 6 find the original numbers

Answer 1

Two numbers are such that the ratio between them is 3:5.
If each is increased by 10, the ratio between the new numbers so formed is 5:7.
find the original numbers.
:
Let x = the multiplier
then
3x = one number
5x = the other number
:
"If each is increased by 10, the ratio between the new numbers so formed is 5:7."

Cross multiply
5(5x+10) = 7(3x+10)
:
25x + 50 = 21x + 70
25x - 21x = 70 - 50
4x = 20
x = 20/4
x = 5 is the multiplier
then
3(5) = 15 is the 1st number
5(5) = 25 is the 2nd number 

Answer 2

Let the numbers be 3a and 4a

According to question,

( 3a + 16) / (4a + 16) = 5 / 6

=> 18a + 96 = 20a + 80

=> 2a = 16

=> a = 8

First number = 8 × 3 = 24

Second number = 8× 4 = 32