Question

A student was getting the following four offers on the purchase of a book:

I - Two successive discounts of 20% and 20%

Il - Two successive discounts of 25% and 15%

Ill - Two successive discounts of 30% and 10%

IV - Two successive discounts of 5% and 35%

Which scheme offers the most discount to the student?

• A. III
• B. II
• C. IV
• D. I

Answer 1

Answer:

C. IV

To find which scheme gives the maximum discount, compute the net discount for successive discounts using:

$\text{Net Discount} = a + b - \frac{ab}{100}$

(where (a%) and (b%) are successive discounts)

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I: 20% and 20%
$20 + 20 - \frac{20 \times 20}{100} = 40 - 4$= 36%

II: 25% and 15%

$25 + 15 - \frac{25 \times 15}{100} = 40 - 3.75$ = 36.25%

III: 30% and 10%

$30 + 10 - \frac{30 \times 10}{100} = 40 - 3$ = 37%

IV: 5% and 35%

$5 + 35 - \frac{5 \times 35}{100} = 40 - 1.75$= 38.25%

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Maximum discount is offered by Scheme IV (38.25%)