The cost price of a television is Rs 11,000. It is marked a% above its cost price. A shopkeeper allows two successive discounts of Rs 350 and 10% respectively and sells it at a profit of Rs 2,050. The cost price of another television is 15% less than the cost price of the first television. If the second television is sold for Rs 11,220 at (a −
b)% profit, find the value of
b.

ATQ, Cost price of the first television = Rs 11,000. Profit on the first television = Rs 2,050. Selling price of the first television = 11,000 + 2,050 = Rs 13,050. The shopkeeper gives two successive discounts of Rs 350 and 10%. Let the marked price of the first television be Rs M. After discount of Rs 350, price = M − 350. After 10% discount, selling price = 90% of (M − 350). So, (M − 350) × 90/100 = 13,050. M − 350 = 13,050 × 100/90. M − 350 = 13,050 × 10/9. M − 350 = 14,500. M = 14,500 + 350 = Rs 14,850. Markup above cost price = 14,850 − 11,000 = Rs 3,850. a = 3,850 × 100/11,000. a = 35. Cost price of the second television is 15% less than Rs 11,000. Cost price of second television = 11,000 × 85/100 = Rs 9,350. Selling price of second television = Rs 11,220. Profit = 11,220 − 9,350 = Rs 1,870. Profit percentage = 1,870 × 100/9,350. Profit percentage = 20%. Given profit percentage = (a − b)%. So, a − b = 20. 35 − b = 20. b = 15.