Question

Two numbers are such that the ratio between them is 3:5 If each is increased by 5, the ratio between the new numbers so formed is 2:3 Find the original numbers.

Answer 1

Answer:

Given:-

• Two numbers are such that the ratio between them is 3:5.

• It is increased by 5. So, the ratio between the new numbers so formed is 2:3.

To Find:-

• The original numbers.

Solution:-

• Let the numbers be 2x & 3x

ATQ,

(x + 5) : (y + 5) = 2 : 3

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

⇒ 3(3x + 5) = 2 (5x+ 5)

⇒ 9x + 15 = 10x + 10

⇒ 9x - 10x = 10 - 15

⇒ -x = -5

⇒ x = 5

Hence, the original numbers are :-

• 2x = 2 × 5 = 10
• 3x = 3 × 5 = 15

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Answer 2

$\sf{\huge{\underline{\orange{Given :-}}}}$

• Two numbers are such that the ratio between them is 3:5.

• Each is increased by 5, the ratio between the new numbers so formed is 2:3.

$\sf{\huge{\underline{\pink{To\:Find :-}}}}$.

• The original numbers.

$\sf{\huge{\underline{\red{Answer :-}}}}$

Two numbers are such that the ratio between them is 3:5.

x : y = 3:5

➝ 5x = 3y

➝ x = 3/5y

(x+5) : (y+5) = 2 : 3

➝ $\dfrac{(x + 5)}{(y + 5)} = \dfrac{2}{3}$

➝ 3(x+5) = 2(y+5)

➝ 3x + 15 = 2y + 10

➝ 3x - 2y = 10 - 15

➝ 3x - 2y = -5 ----(1)

➝ 3×3/5y - 2y = -5

➝ 9/5 y - 2y = -5

➝ (9-10)/5 y = -5

➝ -y = -25

➝ y = 25

From ( 1 ) equation,

3x - 2y = -5

➝ 3x - 2× 25 = -5

➝ 3x- 50 = -5

➝ 3x = -5 + 50

➝ 3x = 45

➝ x = 45/3

➝ x = 15

The original numbers are 15 & 25 .