Question

two numbers are in ration2:3 if 5 is added to each number then the ratio becomes 5:7 find the number​

Answer 1

Answer:

The numbers are 20 & 30.

Step-by-step-explanation:

Let the first number be x.

And the second number be y.

From the first condition,

The ratio of first number to second number is 2 : 3.

∴ x : y = 2 : 3

⇒ x / y = 2 / 3

⇒ x = ( 2 / 3 ) * y

⇒ x = 2y / 3 - - ( 1 )

Now, from the second condition,

When 5 is added to both the numbers, ratio becomes 5 : 7.

∴ ( x + 5 ) : ( y + 5 ) = 5 : 7

⇒ ( x + 5 ) / ( y + 5 ) = 5 / 7

⇒ ( x + 5 ) * 7 = 5 * ( y + 5 )

⇒ 7x + 35 = 5y + 25

⇒ 7x - 5y = 25 - 35

⇒ 7x - 5y = - 10

⇒ 7 * ( 2y / 3 ) - 5y = - 10

⇒ ( 14y / 3 ) - 5y = - 10

⇒ ( 14y - 3 * 5y ) / 3 = - 10

⇒ ( 14y - 15y ) / 3 = - 10

⇒ 14y - 15y = - 10 * 3

⇒ - y = - 30

⇒ y = 30

Now, by substituting y = 30 in equation ( 1 ), we get,

x = 2y / 3 - - ( 1 )

⇒ x = ( 2 * 30 ) / 3

⇒ x = 60 ÷ 3

⇒ x = 20

∴ The numbers are 20 & 30.

Answer 2

Answer :-

• Numbers are 20 and 30.

Given :-

• Two numbers are in ration2:3 If 5 is added to each number then the ratio becomes 5:7.

To Find :-

• The numbers.

Solution :-

Put x in the ratio

→ Numbers are :-

• 2x
• 3x

→ 5 added to each :-

• 2x + 5
• 3x + 5

→ When 5 added to each, the ratio becomes 5:7

According to question :-

2x + 5/3x + 5 = 5/7

→ 7 (2x + 5) = 5 (3x + 5)

→ 14x + 35 = 15x + 25

→ 35 - 25 = 15x - 14x

→ x = 10

Put the value of x in the ratio

• 2x = 2 × 10 = 20
• 3x = 3 × 10 = 30

Hence, the numbers are 20 and 30.