The cost price of a gadget is Rs 8,000. It is marked a% above its cost price. A trader offers two successive discounts of Rs 200 and 10% respectively and sells it at a profit of Rs 820. The cost price of another gadget is 20% less than the cost price of the first gadget. If the second gadget is sold for Rs 7,360 at (a −
b)% profit, find the value of
b.

ATQ, Cost price of the first gadget = Rs 8,000. Profit on the first gadget = Rs 820. Selling price of the first gadget = 8,000 + 820 = Rs 8,820. The trader gives two successive discounts of Rs 200 and 10%. Let the marked price of the first gadget be Rs M. After discount of Rs 200, price = M − 200. After 10% discount, selling price = 90% of (M − 200). So, (M − 200) × 90/100 = 8,820. M − 200 = 8,820 × 100/90. M − 200 = 8,820 × 10/9. M − 200 = 9,800. M = 9,800 + 200 = Rs 10,000. Markup above cost price = 10,000 − 8,000 = Rs 2,000. a = 2,000 × 100/8,000. a = 25. Cost price of the second gadget is 20% less than Rs 8,000. Cost price of second gadget = 8,000 × 80/100 = Rs 6,400. Selling price of second gadget = Rs 7,360. Profit = 7,360 − 6,400 = Rs 960. Profit percentage = 960 × 100/6,400. Profit percentage = 15%. Given profit percentage = (a − b)%. So, a − b = 15. 25 − b = 15. b = 10.