Question : A shopkeeper offers the following discount schemes for buyers in an article:
i. Two successive discounts of $15 \%$ each
ii. A discount of $\mathrm{25 \%}$ followed by a discount of $5 \%$
iii. Two successive discounts of $20 \%$ and $10 \%$
iv. A discount of $30 \%$
Under which scheme will the selling price be maximum?
Option 1: Scheme iv
Option 2: Scheme iii
Option 3: Scheme ii
Option 4: Scheme i
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Correct Answer: Scheme i
Solution :
i. Two successive discounts of $15 \%$ each
Single equivalent discount $= a+b–\frac{a×b}{100} =15 + 15 -\frac{15\times 15}{100}=30-2.25=27.75\%$
ii. A discount of $\mathrm{25 \%}$ followed by a discount of $5 \%$
Single equivalent discount $=25 + 5 -\frac{25\times 5}{100}=30-1.25=28.75\%$
iii. Two successive discounts of $20 \%$ and $10 \%$
Single equivalent discount $=20 + 10 -\frac{20\times 5}{100} = 30 - 1 =29\%$
iv. A discount of $30 \%$
If the discount is minimum, then the selling price is maximum.
The selling price is maximum in scheme (i).
Hence, the correct answer is scheme i.
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