Chapter 9 Commercial Mathematics Ex 9.2 Solutions

Cost price (C.P.) = ₹ 24000 Selling price (S. P.) = ₹ 30,000 Profit = S.P. – C.P. = 30,000 – 24,000 = 6,000 ∴ Profit Percentage = 25%

C.P. of mobile phone = ₹ 18,000 Profit percentage on mobile phone = 20% Selling price (S.P.) of mobile phone = 18,000 (1 + ) = 18,000 (1 + ) = 18,000 × = ₹ 21,600 C.P. of refrigerator = 15,000 Loss percentage on refrigerator = 20% ∴ Selling price (S.P.) = 15,000(1 – ) = 15,000(1 – ) = 15,000 × = ₹ 12,000 ∴ Total gelling price for the transaction = 21,600 + 12,000 = ₹ 33,600 Total cost price (purchase price) for the transaction = 18,000 + 15,000 = ₹ 33,000 ∴ Overall profit made by Shraddha = Total S.P. – Total C.P. = 33,600 – 33,000 = ₹ 600 Thus, Shraddha made on overall profit of ₹ 600.

Vendor bought toffees at the rate of 6 for ₹ 10 ∴ Cost price of one toffee = i.e. C.P. = …….(i) Let x be the number of toffees he must sell in ₹ 10 to gain 20% i.e. S.P. = …….(ii) Profit percentage = Using (i) and (ii) we have ∴ 30(6 – x) = 6x ∴ 180 – 30x = 6x ∴ 36x = 180 ∴ x = 5 The vendor must sell 5 toffees for ₹ 10 in order to gain 20%.

Let x be C.P. of the article Let y % be both, the gain and loss made when article is sold at ₹ 2,880 and ₹ 1,920 respectively. Then x + x = 2880 ……(i) x – x = 1920 …..(ii) Adding (i) and (ii), we get 2x = 4800 ∴ x = 2400 i.e. C.P. of the article = ₹ 2400 Required profit percentage = 25% ∴ The article should be sold at ₹ 3000 to earn 25% profit.

Let the cost price of the cloth be ₹ ‘x’ per meter He claims a loss of 4% ∴ Selling price of the cloth S.P. = C.P.(1 – ) = x(1 – ) = 0.96x …..(i) The actual cost price of the cloth is lower as the cloth is measured by a faulty meter scale. Given that shopkeeper’s profit = 20% ∴ The actual cost price is 0.8 times the cost price as advertised. In other words, the meter scale used for the fraud is 0.8 times the meter scale that should have been used. ∴ The length of the faulty meter scale used = 0.8 × 1 = 0.8 meter ∴ The actual length of the scale is 0.8 meters.

Sunil sells his bike to Rohit at 20% profit. So S.P. of the bike for Sunil = 25000 + × 25000 = 25000 + 5000 = 30000 ∴ Cost price of bike to Rohit = ₹ 30000 Rohit sells the bike back to Sunil at 20% loss ∴ S.P. of the bike for Rohit = 30000 – × 30000 = 30000 – 6000 = 24000 ∴ In second transaction Sunil pays 24000 to Rohit In the first transaction, he had received 30000 from Rohit ∴ Sunil made a profit of ₹ (30000 – 24000) = ₹ 6000 Sunil earned this profit on the bike which costed him ₹ 25000 ∴ Total profit % that Sunil makes = × 100 = = 24 ∴ Sunil makes 24% profit considering both the transactions.

S.P. = ₹ 405 Loss% = 25 S.P. when there is a loss is given by S.P. = C.P. × ∴ The cost price of the book is ₹ 540.

C.P. = ₹ 675 Loss% = 20% ∴ Loss made in selling = × 675 = ₹ 135 S.P. = C.P. – Loss = 675 – 135 = ₹ 540 Let C.P. be x % S.P., Then 675 = × 540 ∴ x = = 125 ∴ Cost price is 125% of the selling price.

C.P. = ₹ 500 Marked price = C.P. + × C.P. = × 500 = 500 + 75 × 5 = 500 + 375 = 875 25% discount was given on marked price ∴ Discount = × 875 = Selling price = marked price – discount ∴ Ashwin makes 31.25% profit.

Let ₹ x be the cost price of the mixer. The cost price of the refrigerator = x + x = x + 6x = 7x Total cost price =12400 …..[Given] i.e. x + 7x = 12400 i.e. 8x = 12400 ∴ x = = 1550 ∴ The cost price of mixer is ₹ 1550.

Let the marked price be ₹ 100 After 1st discount the price = 100(1 – ) = 95 After 2nd discount the price = 95(1 – ) = After 3rd discount the price = = = = 80.3985 ~ 80.4 Selling price after 3 discounts is ₹ 80.4 Single equivalent discount = Marked price – Selling price = 100 – 80.4 = ₹ 19.6 ∴ Single equivalent discount is 19.6%.

Marked price = ₹ 390 After the first discount of 10%, the price of the shirt ∴ x = 50 ∴ Second discount is 50%

Let ₹ ‘x’ be the list price of the article. Amar gives a discount of 25% on the list price. ∴ Selling price for Amar = = = ₹ Amar sells the article to Akbar Cost price of article for Akbar = ₹ ……(i) Akbar sells the article to Anthony at 10% discount on list price ∴ Selling price for Akbar = = = ₹ …..(ii) Profit percentage = Using (i) and (ii), we have the profit percentage for Akbar as, ∴ Akbar gets a profit of 20% on his cost price.

Let ₹ ‘x’ be the C.P. of the article ∴ Article was sold at 25% profit ∴ S.P. of the article = = = 1.25x If the article was bought at 10% loss i.e., the new C.P. = = = 0.9x and sold at ₹ 7 less ∴ New S.P. = 1.25x – 7 Then, the profit would have been 35% Using profit percentage = ∴ Cost price of the article is ₹ 200

Let x, y be the C.P. of two cars. S.P. of both the cars = 39,10,000 …..[Given] ∴ One car is sold at 15% loss ∴ S.P. of the first car = x – x ∴ x = 39,10,000 ∴ x = ∴ x = 46,000 × 100 ∴ x = 46,00,000 Other car is sold at 15% gain ∴ S.P. of second car = y + y ∴ y + y = 39,10,000 ∴ y = 39,10,000 ∴ y = ∴ y = 34,000 × 100 ∴ y = 34,00,000 x + y = Total C.P. of two cars = 46,00,000 + 34,00,000 = 80,00,000 Total S.P. = 39,10,000 + 39,10,000 = 78,20,000 ∴ S.P. < C.P. ∴ There is a loss of ₹ (80,00,000 – 78,20,000) = ₹ 1,80,000 ∴ Loss % = = = 2.25 ∴ Mr. Mehta bears a 2.25% loss in the whole transaction.