Select the correct answerThe digit at the unit’s place of a two-digit number is increased by 50%. And the digit at the ten’s place of the same number is increased by 100%. Now, we find the new numbers is 33 more than original number. Find the original number.Options3635636264

Let's solve this step by step:

1. Let's assume the original two-digit number is 10x + y, where x is the digit at the ten's place and y is the digit at the unit's place.

2. According to the problem, the digit at the unit’s place (y) is increased by 50%. So, the new unit’s place digit is 1.5y.

3. The digit at the ten’s place (x) is increased by 100%. So, the new ten’s place digit is 2x.

4. The new number is 33 more than the original number. So, we can write the equation as: 10(2x) + 1.5y = 10x + y + 33.

5. Simplifying the equation, we get: 20x + 1.5y = 10x + y + 33.

6. Further simplifying, we get: 10x + 0.5y = 33.

7. This equation implies that x and y must be integers because they are digits of a number. Also, 0.5y must be an integer, which means y must be even.

8. Now, let's check the options one by one:

   • Option 1: 36. Here, x=3 and y=6. Substituting these values in the equation, we get: 103 + 0.56 = 33, which is true. So, 36 is the original number.

   • Option 2: 35. Here, y=5, which is not even. So, 35 cannot be the original number.

   • Option 3: 63. Here, x=6 and y=3. Substituting these values in the equation, we get: 106 + 0.53 = 63, which is not equal to 33. So, 63 cannot be the original number.

   • Option 4: 62. Here, y=2, which is even. But, substituting x=6 and y=2 in the equation, we get: 106 + 0.52 = 62, which is not equal to 33. So, 62 cannot be the original number.

   • Option 5: 64. Here, y=4, which is even. But, substituting x=6 and y=4 in the equation, we get: 106 + 0.54 = 64, which is not equal to 33. So, 64 cannot be the original number.

So, the correct answer is 36.