ABHYAS PREP: COMMERCIAL ARITHMETIC · PROFIT, LOSS & DISCOUNT

Successive discounts: one equivalent discount

Two discounts never add up: the second one applies to the already reduced price. Multiply the “what is left” fractions.

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Worked examples

Example 1 · level 1

A shop gives successive discounts of 10%, then 50% on the marked price. What single discount is equivalent?

50%
55%
60%
65%

Show solution

Fractions left: 0.9 × 0.5 = 0.45.
So 45% of the marked price is paid.
Equivalent single discount = 100% − 45% = 55%.

Answer: 55%

Example 2 · level 2

A shop gives successive discounts of 15%, then 5% on the marked price. What single discount is equivalent?

15%
19.25%
20%
20.75%

Show solution

Fractions left: 0.85 × 0.95 = 0.8075.
So 80.75% of the marked price is paid.
Equivalent single discount = 100% − 80.75% = 19.25%.

Answer: 19.25%

Example 3 · level 3

A shop gives successive discounts of 15%, then 30%, then 5% on the marked price. What single discount is equivalent?

40.5%
43.48%
49.5%
50%

Show solution

Fractions left: 0.85 × 0.7 × 0.95 = 0.5652.
So 56.52% of the marked price is paid.
Equivalent single discount = 100% − 56.52% = 43.48%.

Answer: 43.48%