Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is __________.Choices:- 27 33 49 55

Let's denote the two numbers as 3x and 5x, where x is a common multiplier.

According to the problem, if 9 is subtracted from each of the numbers, the ratio becomes 12 : 23.

So, we can write the equation as follows:

(3x - 9) / (5x - 9) = 12 / 23

Cross-multiplying gives us:

23 * (3x - 9) = 12 * (5x - 9)

Expanding both sides gives:

69x - 207 = 60x - 108

Subtracting 60x from both sides gives:

9x = 99

Finally, solving for x gives:

x = 99 / 9 = 11

So, the smaller number is 3x = 3 * 11 = 33.

Therefore, the smaller number is 33.

Let's solve this step by step:

Step 1: Let's assume the two numbers are 3x and 5x (x is a common multiplier).

Step 2: According to the problem, if 9 is subtracted from each of the numbers, the new numbers are in the ratio 12:23. So, we can write this as:

(3x - 9) / (5x - 9) = 12 / 23

Step 3: Cross multiply to solve for x:

23 * (3x - 9) = 12 * (5x - 9)

69x - 207 = 60x - 108

Step 4: Simplify the equation to solve for x:

69x - 60x = 207 + 108

9x = 315

x = 315 / 9

x = 35

Step 5: Substitute x = 35 into 3x to find the smaller number:

3 * 35 = 105

So, the smaller number is 105. However, this option is not available in the choices provided. There might be a mistake in the problem or the choices.