Question

Two numbers are in the rato
3:5. It 9 is subtracted from each,
the new numbers are in the
ratio 12:23, the smaler number is:​

Answer 1

Answer:

The smaller number is 33.

Step-by-step explanation:

Given :

Ratio of the numbers - 3 : 5

New ratio when 9 is subtracted from each - 12 : 23

To find :

The smaller number

Solution :

Let the numbers be -

• 3y
• 5y

According to the question,

⇒ 3y + 9 : 5y + 9 = 12 : 23

⇒ (3y + 9)/(5y + 9) = 12/23

⇒ 23(3y + 9) = 12(5y + 9)

⇒ 69y + 207 = 60y + 108

⇒ 69y - 60y = 207 - 108

⇒ 9y = 99

⇒ y = 99/9

⇒ y = 11

★ Smaller number :

⇒ 3(11)

⇒ 33

Therefore, the smaller number is 33.

Answer 2

$\huge\sf{Answer:}$

☆ Given:

⇏ Two numbers are in the rato 3:5. It 9 is subtracted from each, the new numbers are in the ratio 12:23.

☆ Find:

⇏ Find the smaller number.

☆ According to the question:

⇏ Let us assume 3x and 5y as numbers.

☆ Calculations:

⇏ $\sf [(3x + 9) : (5y + 9)] = 12 : (23)$

⇏ $\sf \dfrac{(3x + 9)}{(5y + 9)} = \dfrac{12}{23}$

⇏ $\sf [23 \: (3x + 9) = 12 \: (5y + 9)]$

⇏ $\sf [(69x + 207 )= (60y + 108)]$

⇏ $\sf [(69x - 60y) = (207 - 108)]$

⇏ $\sf 9x = 99$

⇏ $\sf x = \dfrac{99}{9}$

⇏ ${\sf{\underline{\boxed{\sf{x = 11}}}}}$

☆ Finding the smaller number:

⇏ $\sf 3 × 11$

⇏ ${\sf{\underline{\boxed{\sf{33}}}}}$

Therefore, 33 is the smaller number.