Question

two number are such that the ratio between them is 3:5 if it is increased by 10 the ratio between the new number so formed is 5:7 find original numbers​

Answer 1

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 .

⚡⚡Hope it will help you.⚡⚡

Answer 2

Answer:

Step-by-step explanation:

Given :-

The ratio of 3:5 is increased by 10 the ratio between the two numbers so form does 5:7.

To Find :-

The original number

Solution :-

Let the first number is x, the second is y.

⇒ 5x = 3y

⇒  (x + 10)7 = (y + 10)5

⇒ 7x + 70 = 5y + 50

⇒  7x + 20 = 5y

⇒  x = 3/5y  -------- (i)

⇒  7 × 3/5y + 20 = 5y

⇒  21y + 100 = 25y

⇒  4y = 100

⇒  y = 25

Putting y value in euation (i), we get

x = 3/5 × 25

x = 15

Hence, the original  numbers are 15 and  25.