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

3(5) = 15 is the 1st number

5(5) = 25 is the 2nd number

Step-by-step explanation:

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.

Let x

3x = one number

5x = the other number

A/q

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

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

Cross multiply

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

25x + 50 = 21x + 70

25x - 21x = 70 - 50

4x = 20

x = 20/4

x = 5

Hence ,

3(5) = 15 is the 1st number

5(5) = 25 is the 2nd number

Step-by-step explanation:

→ 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 .

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