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CH-02-001 · Reverse percentage, VAT and profit margin

A shop reduces the marked price of a machine by 10%, then adds 20% VAT to the reduced price. The customer pays £874.80. The machine cost the shop £199. VAT is passed to the government. Find the marked price and the shop’s profit as a percentage of its cost. Give the percentage to 1 decimal place.

Reverse Percentages, VAT & Profit Margin Booklet p. 52 & p. 53
Method
1) Divide by 1.20 to remove 20% VAT
2) Divide by (100 − discount)/100 for marked price
3) Profit % = ((Net − Cost) ÷ Cost) × 100
Worked Example (CH-02-001)
Booklet p. 53 (Reverse %): Call Original x  ⇒  x×(100±%100)=New Amount\mathbf{x} \;\Rightarrow\; \mathbf{x \times \left(\frac{100 \pm \%}{100}\right) = \text{New Amount}} (Divide both sides by multiplier!)
1) Remove VAT: £874.80 ÷ 1.20 = £729.00.
2) Divide this by 0.90.
3) Marked price £810.00.
4) Profit excluding VAT = £530.00; divide by the cost £199 and multiply by 100.
5) 266.3%.
Marked price £810.00; profit 266.3%.