Question

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.

Answer 1

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."
= 3x+10/5x+10 = 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

Here is your answer

Since the ratio between the numbers is 3:5. So, let the two numbers be 3x and 5x.

If each number is increased by 10 the new number are 3x + 10 and 5x + 10.

It is given that the ratio between the New numbers is 5:7.


$\frac{3x + 10}{5x + 10} = \frac{5}{7} \\ \\ = > 7 \times (3x + 10) = 5 \times (5x + 10) \\ \\ = > 21x + 70 = 25x + 50 \\ \\ = > 21x - 25x = 50 - 70 \\ \\ = > - 4x = - 20 \\ \\ = > x = \frac{ - 20}{ - 4} = 5$


Hence, the two numbers are 3x = 3 × 5 = 15 and 5x = 5 × 5 = 25 .



Hope it helped ☺☺☺☺