Discussion
Ramesh was offered two schemes on a book having a marked price of Rs. 800: either two successive discounts of 20% each, or two successive discounts of 30% and 10%. If Ramesh chose the better scheme, how much more did he save compared with the other one?
Answer: C
Compare the two schemes by the fraction of the price that survives them.
20% then 20%:
\[ 800 \times 0.80 \times 0.80 = 800 \times 0.64 = \text{Rs. } 512 \]
30% then 10%:
\[ 800 \times 0.70 \times 0.90 = 800 \times 0.63 = \text{Rs. } 504 \]
\[ \text{extra saving} = 512 - 504 = \text{Rs. } 8 \]
Both schemes total 40% on paper, yet the more lopsided split wins. In general \( (1-a)(1-b) = 1 - a - b + ab \), so for a fixed sum \( a+b \) the retained fraction shrinks as the product \( ab \) shrinks - and \( 0.30 \times 0.10 = 0.03 \) is smaller than \( 0.20 \times 0.20 = 0.04 \).
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