Question

The result of dividing two digit number by the number with digits reversed is `1 3/4` and the sum of the digits of number is 9. Find the number.

Answer 1

Given:

• A two-digit number is divided by the number formed by reversing its digits, resulting in `1 3/4` which is `7/4`.
• The sum of the digits of the two-digit number is 9.

Step-wise calculation:

1. Let the two-digit number be 10x + y, where (x) and (y) are digits.

2. The number with digits reversed is 10y + x.

3. According to the problem:

`(10x + y)/(10y + x) = 7/4`

4. The sum of the digits is x + y = 9.

Thus, y = 9 – x.

5. Substitute (y = 9 – x) into the ratio equation:

`(10x + y)/(10y + x) = 7/4` 

4(10x + y) = 7(10y + x) 

40x + 4y = 70y + 7x 

40x – 7x = 70y – 4y 

33x = 66y 

33x = 66(9 – x) 

33x = 594 – 66x 

33x + 66x = 594 

99x = 594 

`x = 594/99`

x = 6

6. Find (y):

y = 9 – 6

y = 3

7. Thus, the two-digit number is:

10x + y = 10 × 6 + 3

10x + y = 63

8. Verify the division ratio:

`63/36 = 7/4`

`63/36 = 1.75`

`63/36 = 1 3/4`

The two-digit number is 63.