Question

(+10)
24. Two numbers are such that the ratio between them is 3:5. If each, increased by 10, the
ratio between the new number formed is 5:7. Find the original numbers.​

Answer 1

Answer:

let no. be 3x and 5x

(3x+10)/(5x+10)=5/7

21x+70=25x+50

4x=20

x=5

so numbers are 15 and 25

Answer 2

Answer:

let the original numbers be x and y.

x:y= 3:5

x/y=3/5

5x=3y

5x-3y=0-(i)

x+10:y+10=5:7

x+10/y+10= 5/7

by cross-multiplication

7(x+10)=5(y+10)

7x+70= 5y+50

7x-5y=70-50

7x-5y=20-(ii)

We have to get a single variable so multiply equation (i) by 5 and multiply equation (ii) by 3.

5(5x-3y)= 5(0)

25x-15y=0-(iii)

3(7x-5y)=3(20)

21x-15y=60-(iv)

Upon subtracting (iv) from (iii), we get

25x-15y=0

21x-15y=60

-    +       -    

4x + 0 = -60

4x=-60

so x=-60/4= -15

and 5x-3y=0 - (i)

so, by substituting the value of x, we can find the value of y

5(-15) - 3y=0

-75 - 3y=0

-3y=75

y= 75/-3 = -25

Thus, the original numbers were x=-15 and y=-25

Hope that I helped. Please mark me as brainliest.