A shopkeeper offers the following schemes on toys of the same marked price. (A) Successive discounts of 44% and 12% on any number of toys bought. (B) Successive discounts of 18%, 43% and 23% on any number of toys bought. (C) 8% discount on the first 4 toys and 38% discount on each toy thereon. (D) On buying ten items, the customer is billed for only seven items. A customer wants to buy 10 toys. Which of the above schemes is the least beneficial to her?
C
The least beneficial scheme is the one that leaves the customer paying the highest total for 10 toys. Take each toy's marked price as 1 unit, so 10 toys are worth 10 units, and find the amount payable under each scheme.
Scheme A: two successive discounts of 44% and 12% give a paid fraction \(0.56 \times 0.88 = 0.4928\), so the customer pays \(0.4928 \times 10 = 4.928\) units.
Scheme B: three successive discounts of 18%, 43% and 23% give \(0.82 \times 0.57 \times 0.77 = 0.35996\), so the customer pays \(0.35996 \times 10 = 3.5996\) units.
Scheme C: the first 4 toys carry 8% discount, i.e. \(4 \times 0.92 = 3.68\) units; the remaining 6 toys carry 38% discount, i.e. \(6 \times 0.62 = 3.72\) units. Total paid \(= 3.68 + 3.72 = 7.4\) units.
Scheme D: pay for only 7 of the 10 toys, so the customer pays \(7\) units.
Comparing the amounts payable: A = 4.928, B = 3.5996, C = 7.4, D = 7. Scheme C makes the customer pay the most (7.4 units).
Hence, the least beneficial scheme is C.
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Important Questions from Discount and MP
A single discount equivalent to two successive discounts of 15% and 25% is:
Ramesh purchases 75 articles for ₹ 10800 and sells them at a loss equal to the selling price of 5 articles. What will be the selling price of one article?
A TV was available for Rs. 14,500. The price came down to Rs. 11,890 during the Diwali sale. What is the percentage discount?
A shopkeeper marks the marked price of an article 30% more than its real price and offers 10% discount. What is the gain percentage?
An article was sold for Rs. 1,215 after giving a discount of 19%. If a discount of 17.5% is given, then for how much (in Rs.) should the article be sold?
