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

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 x and y

ATQ
x/y = 3/5
5x - 3y = 0 ---(1)
x = 3y/5
also,
x+10 / y+ 10 = 5/7
5y + 50 = 7x + 70
5y - 7x = 20 ----(2)
from 1 and 2
put value of x in eq 2
5y - 7(3y/5) = 20
5y - 21y/5 = 20
25y -21y / 5 = 20
4y/5 = 20
4y = 100
y = 25
x = 3 x 25 / 5
x = 15