Question

two numbers are such that the ratio between them is a 3 ratio 5. if each is increased by 10 the ratio between the new number so formed is 5 ratio 7.find the original numbers

Answer 1

Hi ,

let x , y are two numbers

x : y = 3 : 5

5x = 3y

x = 3y / 5 -----( 1 )

according to the problem given ,

if each is increased by 10 , the ratio between

the new numbers so formed is 5 : 7

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

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

7x + 70 = 5y + 50

7x + 70 - 50 = 5y

7x + 20 = 5y----( 2 )

substitute x value from equation ( 1 ) in ( 2 )

7× 3y/5 + 20 = 5y

( 21y + 100 ) / 5 = 5y

21y + 100 = 25y

100 = 25y - 21y

100 = 4y

100 / 4 = y

25 = y

Therefore ,

y = 25

put y = 25 in equation ( 1 ), we get

x = 3 × 25 / 5

x = 3 × 5

x = 15

Original numbers are x and y

= 15 and 25

I hope this helps you.

Answer 2

Let the numbers be 3x and 5x

Therefore, $\frac{3x+10}{5x+10}$ = $\frac{5}{7}$


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

21x + 70 + 25x + 50

25x - 21x = 70 - 50

4x = 20

x = $\frac{20}{4}$

x = 5



1st number = 3x = 3 × x = 3 × 5 = 15

2nd number = 5x = 5 × x = 5 × 5 = 25