Numerical answer
A trader lists a product at 60% above its cost price. He offers a first discount of 15% on the listed price, followed by a second discount of y% on the reduced price. If his net profit works out to 22.4%, find the value of y.
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Answer: 10
Let CP = 100. Marked price = 160. After the first discount of 15%: 160 × 0.85 = 136.
Final selling price must give a 22.4% profit, so it equals 122.4. Thus 136 × (1 − y/100) = 122.4, giving 1 − y/100 = 122.4/136 = 0.9, i.e. y = 10.
Tip: Work with CP = 100 and multiply successive factors (1.6 × 0.85 × (1 − y/100) = 1.224); percentage chains are products of multipliers, not sums.
Final selling price must give a 22.4% profit, so it equals 122.4. Thus 136 × (1 − y/100) = 122.4, giving 1 − y/100 = 122.4/136 = 0.9, i.e. y = 10.
Tip: Work with CP = 100 and multiply successive factors (1.6 × 0.85 × (1 − y/100) = 1.224); percentage chains are products of multipliers, not sums.
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