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a two digit number is such that the product of its digit is 35 when 18 is added to the number the digit interchange their places find the number
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Problem Statement

A two-digit number is such that the product of its digits is 35. When 18 is added to the number, the digits interchange their places. Find the number.


Solution


Step 1: Finding the possible two-digit numbers

We need to find a two-digit number where the product of its digits is 35. The possible two-digit numbers are:



  • 1 × 35 = 35

  • 5 × 7 = 35



Step 2: Checking the conditions

Now, we need to check which of the two possible numbers satisfies the given condition that when 18 is added to the number, the digits interchange their places.



  • For the number 13, adding 18 gives 31, which does not interchange its digits.

  • For the number 57, adding 18 gives 75, which does interchange its digits.



Step 3: Final Answer

Therefore, the two-digit number is 57.
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a two digit number is such that the product of its digit is 35 when 18 is added to the number the digit interchange their places find the number
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