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

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.

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Answer 2

Let the no be 3x and 5x.

$\frac{3x + 10}{5x + 10} = \frac{5}{7} \\ \\ 5(5x + 10) = 7(3x + 10) \\ \\ 25x + 50 = 21x + 70 \\ \\ 25x - 21x = 70 - 50 \\ \\ 4x = 20 \\ \\ x = \frac{20}{4} \\ \\ x = 5$

Hence, the no are

3x = 3 * 5 = 15

5x = 5 * 5 = 25

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Thank you☺️