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

let the two numbers are x and y
then,
x/y = 3/5
x=(3y) /5. ......(1)

also,
(x+10)/(y+10) = 5/7
7(x+10)=5(y+10)
7x = 5y+50-70=5y-20
put the value of x from eq. (1)
7(3y/5) =5y - 20
21y =25y - 100
25y-21y = 100
y = 100/4
y =25

put the value of y in eq.(1)

x = (3×25)/5
x=15

hence , the numbers are 15 and 25

I hope this will help you...

Answer 2

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 .