Question

Two numbers are In the ratio 2:3.if 5 is added to each number, then the new numbers are in the ratio 3:4. find the numbers.
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Answer 1

Answer:

The numbers are 10 and 15.

Step-by-step explanation:

Let,

• I st number = 2x
• II nd number = 3x

5 is added to each number,

• I st number = 2x + 5
• II nd number = 3x + 5

Also,

The new numbers are in the ratio 3:4

★ According to the Question :

⇒ $\dfrac{2x \: + \: 5}{3x \: + \: 5} \: = \: \dfrac{3}{4}$

⇒ 4 (2x + 5) = 3 (3x + 5)

⇒ 8x + 20 = 9x + 15

⇒ 20 - 15 = 9x - 8x

⇒ 5 = x

⇒ x = 5

___________________________

★ Value of 2x :

⇒ 2 (5)

⇒ 10

I st number = 10

___________________________

★ Value of 3x :

⇒ 3 (5)

⇒ 15

II nd number = 15

Therefore, the numbers are 10 and 15.