# Puzzle 9) Deepak and its two Digit Number

Submitted by Amit Shukla, on August 09, 2017

**Puzzle**

Deepak is an engineering student. He likes to plays with numbers. One day he asked a question to his friend Abhishek. Deepak said that he takes a two-digit integer number. He says that when he multiplies its two- digit integer by the sum of its digits, 405 is achieved. And If he multiplies its number written in reverse order of the same digits by the sum of digits, he get 486. Now Abhishek wants your help to find out the two-digit number taken by Deepak.

**Important points of puzzle:**

- Deepak likes to play with numbers.
- He asked a question to his friend Abhishek.
- Deepak said that he takes a two- digit number.
- Multiplication of two-digit number with sum of its digit is 405.
- Multiplication of two-digit number written in reverse order with sum of digits in reverse order is 486.
- Find out the two- digit integer number.

**Answer**

45.

**Reason**

In these types of problems, we used to find out the factor of 405. As given in problem that number is a two- digit integer, then we search all pairs of factors of 405 which are of two- digit integer. On finding two- digit factors of 405 we got 15 * 27 and 45 * 9. From these factors pairs only the second pair 45 * 9 give us desired result. Because 54 * 9 is 486. Hence the correct answer is 45.

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