Question

Two numbers are in the ratio 8 : 9. If 12 is added to both the numbers, their ratio becomes 12 : 13. Find the numbers.

Answer 1

Given: Two numbers are in the ratio 8 : 9. If 12 is added to both the numbers, their ratio becomes 12 : 13. Find the numbers.

Step-wise calculation:

1. Let the two numbers be (8x) and (9x) because they are in the ratio 8 : 9.

2. Adding 12 to both numbers, the new numbers are (8x + 12) and (9x + 12).

3. The ratio of the new numbers is given as:

`(8x + 12)/(9x + 12) = 12/13`

4. Cross-multiply to solve for (x):

13(8x + 12) = 12(9x + 12)

5. Expand both sides:

104x + 156 = 108x + 144

6. Rearranging:

156 – 144 = 108x – 104x 

12 = 4x

7. Solve for (x):

`x = 12/4`

x = 3

8. Substitute (x = 3) back to numbers: 

8x = 8 × 3

8x = 24 

9x = 9 × 3

9x = 27

The two numbers are 24 and 27 respectively.