Question

The sum of the digits of a two-digit number is 11. The result of subtracting the units digit from the tens digit is 5. What are the two-digit numbers?

The tens digit:
The units digit:

Answer 1

The two digit number is 83

Explanation:

Hi

Assume the 2 digit number as xy. Here x is the tens digit and y is the units/ones digit.

Now apply the given information,

x + y = 11 (i)

x - y = 5 (ii)

Lets add both the equations to create a unified equation.

x + y + x - y = 11 + 5

[as there is a positive y and negative y, adding it will lead to its cancellation]

Thus, x + x = 16

2x = 16

x = 16/2

x = 8

To find y, you have to substitute the value of x to either equation (i) or (ii).

x + y = 11 (i)

8 + y = 11

y = 11 - 8

y = 3

[Even if you apply these to the equation (ii)

x - y = 5

8 - y = 5

y = 8 - 5

y = 3

The answer is same ]

Tens digit = 8

Units digit = 3