Choosing Between Two Discount Schemes with Fine Print
A student needs to buy a laptop with list price ₹24,000. Store A offers a 20% discount, then 10% cashback credited as store points that can be used only on a future purchase, and charges 18% GST on the discounted price. Store B offers a 25% discount, charges 18% GST on the discounted price, and adds a 2% payment-gateway fee on the post-GST amount. The student has no immediate plan to shop again at Store A and values store points at only 50% of face value. A friend says Store B is cheaper because 25% > 20%. The student must compare the real cost, decide which store is cheaper under these assumptions, and determine how much the Store A cashback would need to be worth as a fraction of face value for the two stores to cost the same. Assume no other charges.
1. Compute the nominal payable amount and the effective cost at each store under the student's 50% valuation of store points. Which store is cheaper, and by how much?
Read the worked answer
Store A: Discounted price = 24,000 × 0.80 = ₹19,200. GST = 18% of 19,200 = ₹3,456. Amount payable = ₹22,656. Cashback face value = 10% of 19,200 = ₹1,920. At 50% valuation, cashback benefit = ₹960. Effective cost = 22,656 − 960 = ₹21,696.
Store B: Discounted price = 24,000 × 0.75 = ₹18,000. GST = 18% of 18,000 = ₹3,240. Post-GST amount = ₹21,240. Gateway fee = 2% of 21,240 = ₹424.80. Total payable = ₹21,664.80.
Store B is cheaper by ₹21,696 − ₹21,664.80 = ₹31.20 under the 50% valuation. The friend's comparison is incomplete because the cashback and gateway fee change the effective cost, and the percentages apply to different bases.
2. Find the fraction of the Store A cashback face value at which the two stores would cost the same. Interpret the result.
Read the worked answer
Let f be the fraction of the ₹1,920 cashback that the student values. Then Store A's effective cost is 22,656 − 1,920f.
Set this equal to Store B's cost: 22,656 − 1,920f = 21,664.80 1,920f = 22,656 − 21,664.80 = 991.20 f = 991.20 / 1,920 = 0.51625.
So the two stores cost the same if the cashback is worth about 51.6% of face value. If the student values points above 51.6%, Store A is cheaper; below 51.6%, Store B is cheaper. At the stated 50% valuation, Store B wins narrowly.
3. Explain why the friend's statement "25% is better than 20%" is not a valid comparison here, and give one non-price factor that could reverse the decision.
Read the worked answer
The two discounts are not applied in the same way. Store A's 20% discount is followed by cashback that is not cash and is worth only 50% to this student, and Store A's GST is calculated on a higher discounted price. Store B's 25% discount is larger, but a 2% gateway fee is applied after GST, so the final payable amounts differ by only ₹31.20. Comparing headline percentages ignores the order of operations, the tax base, and the liquidity of the cashback.
A non-price factor such as warranty terms, return policy, delivery time, or the ability to use the laptop immediately could reverse the decision. For example, if Store A offers a longer warranty or faster delivery, the ₹31.20 saving at Store B may not be worth choosing it.