Two number are in the ratio 12 : 13. If 20 is subtracted from each, the new numbers are in the ratio 2 : 3. The smaller number is:a)26b)24c)32d)28Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Let's assume the two numbers in the ratio 12:13 are 12x and 13x, where x is a common factor.

Subtracting 20 from each number gives us the new numbers in the ratio 2:3. So, the new numbers can be represented as 2y and 3y, where y is a common factor.

To solve this problem, we can set up an equation based on the given information:

(12x - 20) / (13x - 20) = 2/3

To simplify this equation, we can cross multiply:

3(12x - 20) = 2(13x - 20)

Expanding both sides of the equation:

36x - 60 = 26x - 40

Bringing like terms to one side:

36x - 26x = -40 + 60

10x = 20

Dividing both sides by 10:

x = 2

Now, we can find the smaller number:

Smaller number = 12x - 20 = 12(2) - 20 = 24 - 20 = 4

Therefore, the smaller number is 24.

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