Answer to Question #31932 in Algebra for vishnupriya

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 the first number is x, the second is y.Then x/y=3/5 , 3y=5x
On the other hand (x+10)/(y+10)=5/7 whence 7(x+10)=5(y+10) .
We get that 3y=5x, 7x+70=5y+50
3y=5x, 5y=7x+20
y=5x/3, y=(7x+20)/5
Then we can find x
5x/3=(7x+20)/5
25x=3(7x+20)
25x=21x+60
4x=60
x=15
Then y=5x/3=5*15/3=25

x=15, y=25