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
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Answer 1

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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

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Original number

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Let the number be 3x and 5x

According to the given condition

Each number is increased by 10 ,the ratio between the new numbers so formed is 5:7

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

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

21x + 70 = 25x + 50

21x - 25x = 50 - 70

- 4x = - 20

x = 20/4 = 5

Hence,

Required numbers

First number = 3x = 15

Second number = 5x = 25

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Answer 2

Step-by-step explanation:

Answer:

→ 15 and 25 .

Step-by-step explanation:

Let x and y be the two numbers .

Now,

CASE 1 .

→ Two numbers are such that the ratio between them is 3 : 5.

A/Q,

∵ x : y = 3 : 5

⇒ 5x = 3y .

∵ x = 3y / 5 ........( 1 ).

CASE 2 .

→ If each number in increased by 10, the ratio between the new number so formed is 5 : 7.

A/Q,

∵ ( x + 10 ) : ( y + 10 ) = 5 : 7 .

⇒ 7( x + 10 ) = ( y + 10 ) 5 .

⇒ 7x + 70 = 5y + 50 .

⇒ 7x + 70 - 50 = 5y .

⇒ 7x + 20 = 5y. ........( 2 ).

Put value of 'x' 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 .

∴ y = 25 .

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 .

Hence, it is solved .