Q1.
You have won a contest. The organisers offer you two options to choose from: Option A: You deposit ₹100 and you get back ₹300. Option B: You deposit ₹1000 and you get back ₹1500. What is the percentage gain each option gives? You can choose any option only once. Which option would you choose? Why?
Answer
Option A: gain = 300 – 100 = ₹200 on a deposit of ₹100
Percentage gain = 200/100 × 100 = 200%
Option B: gain = 1500 – 1000 = ₹500 on a deposit of ₹1000
Percentage gain = 500/1000 × 100 = 50%
Percentage gain = 200/100 × 100 = 200%
Option B: gain = 1500 – 1000 = ₹500 on a deposit of ₹1000
Percentage gain = 500/1000 × 100 = 50%
Which to choose? Option A wins on percentage, but Option B puts more money in your pocket — ₹500 against ₹200. Since you may use an option only once, Option B is the better choice, provided you have ₹1000 to deposit. If you only have ₹100, Option B is not available at all and A is the answer.
Why it happens: A percentage gain tells you how hard each rupee worked, not how many rupees you end up with. Option A quadruples a small stake; Option B adds half again to a large one. If the offer could be repeated, the 200% rate would quickly overtake — ₹100 → ₹300 → ₹900 → ₹2700 in three rounds, while Option B needs ₹1000 up front each time. The “only once” condition is what makes the absolute gain decide it. This is the chapter's warning in a single question: when comparing percentages, always check what whole they refer to.