Question

A shop is sending out a bill for an amount less than £100.The accountant intercharges the two digits and so overcharges the customer by 45.Given that the sum of the two digits is 9,find how much the bill should be.​

Answer 1

The original bill amount should be £27.

Let's define the two-digit number where the tens digit is x and the units digit is y.

According to the problem, the sum of the digits is 9: x + y = 9.

The original number can be expressed as 10x + y.

If the digits are interchanged, the new number will be 10y + x.

The new number overcharges the customer by 45: (10y + x) - (10x + y) = 45.

• Solving the Equations:

Now, let's solve these equations step-by-step:

From the given sum of the digits: x + y = 9. (Equation 1)

From the overcharge equation: (10y + x) - (10x + y) = 45

Simplify the overcharge equation: 10y + x - 10x - y = 45

This simplifies to: 9y - 9x = 45, which simplifies further to: y - x = 5. (Equation 2)

• Now we have two equations:

x + y = 9

y - x = 5

• Adding these two equations eliminates x:

(x + y) + (y - x) = 9 + 5

This gives: 2y = 14

Therefore, y = 7

• Substitute y back into Equation 1:

x + 7 = 9

Therefore, x = 2

The original number is 10x + y = 10*2 + 7 = 27.