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.Options6236633564

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 follows: 10 * 2X + 1.5Y = 10X + Y + 33.

5. Simplifying the equation, we get 10X + Y = 33.

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

   • Option 1: 62. If we put X=6 and Y=2 in the equation, we get 60 + 2 = 62, which is not equal to 33. So, this option is incorrect.

   • Option 2: 36. If we put X=3 and Y=6 in the equation, we get 30 + 6 = 36, which is not equal to 33. So, this option is incorrect.

   • Option 3: 35. If we put X=3 and Y=5 in the equation, we get 30 + 5 = 35, which is not equal to 33. So, this option is incorrect.

   • Option 4: 64. If we put X=6 and Y=4 in the equation, we get 60 + 4 = 64, which is not equal to 33. So, this option is incorrect.

So, none of the options satisfy the given conditions. There seems to be a mistake in the problem or the options provided.