A two digit number is 4 times the sum of its digits and twice the product of its digits.The number is ____.

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Detailed Solution

Concept- If a two-digit number is 4 times the sum of its digits and twice the product of its digits, then the number is 36.
Let us assume the one’s digit to be “a” and the tens digit of the number to be “b”.
Then, the number is

.
As per the given conditions, we will form two separate equations involving “a” and “b”, and solving the equations will give us the values of “a” and “b”. We will then use these values to find out the required number.
Given, the two-digit number is 4 times the sum of its digits, i.e.,

Also given that, the number is twice the product of its digits, i.e.,