Question

two numbers are such that the ratio between them is 5 ratio 8 if each is increased by 10 the ratio between the numbers become 7 ratio 10 find the numbers

Answer 1

Let the two numbers are x and y
then,
x/y = 3/5
x=(3y) /5. ......(1)
also,
(x+10)/(y+10) = 5/7
7(x+10)=5(y+10)
7x = 5y+50-70=5y-20
put the value of x from eq. (1)
7(3y/5) =5y - 20
21y =25y - 100
25y-21y = 100
y = 100/4
y =25
put the value of y in eq.(1)
x = (3×25)/5
x=15
hence , the numbers are 15 and 25

Answer 2

Let 1st no.=X

Let 2nd no.=y

Ratio=5/8

So,x/y=5/8

x=5y/8...(1)

Now,

x+10/y+10=7/10...(2)

Put eq no.(1) in (2)

(5y/8+10)/(y+10)=(7/10)

5y+80/8=7y+70/10

50y+800=56y+560

56y-50y=800-560

6y=240

y=40

So,

As x=5y/8

Put y=40

x=5×40/8

x=25