Question

The units’ digit of a two-digit number is 7 more than the tens’ digit. If 26 is added to the number, the result obtained is five times the sum of the digits. Find the number.

Answer 1

Let the digit in the tens place be x

tens place = x (therefore the value is 10x)
ones place = x + 7
The number is 10x + x + 7

Add 26 to it
10x + x + 7 + 26 = 11x + 33

It is 5 times the sum of the digit
11x + 33 = 5(x + x + 7)
11x 33 = 10x + 35
x = 2
x+ 7 = 2 + 7 = 9

So the number is 29