Question

Q1) At a sale goods are marked down by 5 pence in the pound. What was the original price of an article marked £2.85?

Answer 1

`£2.90` if it is a straight deduction.

`£3.00` if it is a ratio of pence to original pounds

Explanation:

A "discount" OR "markup" is usually calculated as a percentage of an original value. A percentage is the ratio of the change to the original value, times 100 to make a "normalized" (easy to compare) "per cent" (parts in 100). For the calculation of the change, the actual decimal value of the ratio must be used.

The equation for a final price is:
Original Price + (Original Price x increase or decrease ratio)

In this example we have the final price and the amount of the decrease, so this simplifies to:
Final Price = Original Price + Change (negative for markdown, positive for markup)

`P_F = P_O + P_c` ; `2.85 = P_O - 0.05`

`P_O = 2.85 + 0.05 = 2.90`

Now, IF you meant the reduction was 5 pence per original pound, that would be a change of `5/100 = 0.05 = 5%`

In that case we need to know the relative change of 5% in the original price. Similar to the previous calculation:
Final Price = Original Price + Change
where Change in this case is `P_O xx -0.05`

`P_F = P_O + P_c` ; `2.85 = P_O - (P_O xx -0.05)`
`2.85 = P_O xx (1 - 0.05)` ; `2.85 = P_O xx (0.95)`
`P_O = 2.85/0.95 = 3.00`