1. Problem 1: Rajesh's gain or loss percent. - Cost price (CP) of 5 apples = 20 - So, CP of 1 apple = \frac{20}{5} = 4 - Selling price (SP) of 6 apples = 36 - So, SP of 1 apple = \frac{36}{6} = 6 - Gain = SP - CP = 6 - 4 = 2 - Gain percent = \left(\frac{Gain}{CP}\right) \times 100 = \left(\frac{2}{4}\right) \times 100 = 50\% 2. Problem 2: Marked price of the television set. - Let marked price = M - Discount = 20% of M = 0.20M - Price paid after discount = M - 0.20M = 0.80M - Given price paid = 85000 - So, 0.80M = 85000 - M = \frac{85000}{0.80} = 106250 3. Problem 3: Single discount equivalent to successive discounts of 5%, 10%, and 25%. - Successive discount formula: 1 - (1 - d_1)(1 - d_2)(1 - d_3) - Convert percentages to decimals: d_1 = 0.05, d_2 = 0.10, d_3 = 0.25 - Equivalent discount = 1 - (1 - 0.05)(1 - 0.10)(1 - 0.25) - = 1 - (0.95)(0.90)(0.75) - = 1 - 0.64125 = 0.35875 - Equivalent discount percent = 0.35875 \times 100 = 35.875\% \approx 36\% 4. Problem 4: Price of mobile phone inclusive of tax is 13530, tax rate 10%. (i) Original price (before tax): - Let original price = P - Tax = 10% of P = 0.10P - Price inclusive of tax = P + 0.10P = 1.10P - Given price inclusive of tax = 13530 - So, 1.10P = 13530 - P = \frac{13530}{1.10} = 12300 (ii) Amount of tax paid: - Tax = 13530 - 12300 = 1230 Final answers: 1. Gain percent = 50% 2. Marked price = 106250 3. Single equivalent discount = 36% 4. (i) Original price = 12300 (ii) Tax paid = 1230