Question

The ratio of two numbers is 3 :5 if each number is increased by 10 the ratio between the numbers so forward is 5:7 find the two 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 .

Answer 2

Hᴇʀᴇ's Yᴏᴜʀ Aɴsᴡᴇʀ:-

Lᴇᴛ Tʜᴇ Tᴡᴏ Nᴜᴍʙᴇʀs ʙᴇ x Aɴᴅ y.

Tʜᴇɴ,

x/y = 3/5

x = ( 3y )/5 ____ ( 1 )

Aʟsᴏ,

( x + 10 )/( y + 10 ) = 5/7

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

7x = 5y + 50 - 70

= 5y - 20

Pᴜᴛ Tʜᴇ Vᴀʟᴜᴇ ᴏғ x Fʀᴏᴍ ᴇǫ. ( 1 )

7 ( 3y/5 ) = 5y - 20

21y = 25y - 100

25y - 21y = 100

y = 100/4

= 25

Pᴜᴛ Tʜᴇ Vᴀʟᴜᴇ ᴏғ y ɪɴ ᴇǫ. ( 1 )

x = ( 3 × 25 )/5

= 15

Hᴇɴᴄᴇ, Tʜᴇ Nᴜᴍʙᴇʀs Aʀᴇ 15 Aɴᴅ 25.

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