Discussion
Which of the following will yield maximum discount on Rs. 6896?
1) 2 successive discounts of 5% and 5%
2) Single discount of 10%
3) 2 successive discounts of 8% and 2%
Answer: B
Successive discounts multiply rather than add. For discounts \( a \) and \( b \) the price retained is \( (1-a)(1-b) \).
1) 5% then 5%:
\[ 0.95 \times 0.95 = 0.9025 \quad\Longrightarrow\quad \text{discount } 9.75\% \]
2) a single 10%:
\[ 0.90 \quad\Longrightarrow\quad \text{discount } 10\% \]
3) 8% then 2%:
\[ 0.92 \times 0.98 = 0.9016 \quad\Longrightarrow\quad \text{discount } 9.84\% \]
The single 10% is largest, so option 2 wins. Two discounts summing to 10% always fall short of a single 10%, because the second is applied to an already reduced price - the shortfall is the product \( ab \), here 0.25% and 0.16%.
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