1. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
a) No profit, no loss
b) 5%
c) 8%
d) 10%
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{. of 56 kg rice}} \cr & = {\text{ }}Rs.{\text{ }}\left( {26{\text{ }} \times {\text{ }}20{\text{ }} + {\text{ }}30{\text{ }} \times {\text{ }}36} \right) \cr & = {\text{ }}Rs.{\text{ }}\left( {520{\text{ }} + {\text{ }}1080} \right) \cr & = {\text{ }}Rs.{\text{ }}1600 \cr & {\text{S}}{\text{.P}}{\text{. of 56 kg rice}} \cr & = {\text{ }}Rs.{\text{ }}\left( {56{\text{ }} \times {\text{ }}30} \right) \cr & = {\text{ }}Rs.{\text{ }}1680 \cr & \therefore {\text{Gain}} = \left( {\frac{{80}}{{1600}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \cr} $$
2. The ratio of the cost price and selling price is 5 : 4, the loss percent is = ?
a) 20%
b) 25%
c) 40%
d) 50%
Explanation:
$$\eqalign{ & \frac{{{\text{Cost price}}}}{{{\text{Selling price}}}} = \left. {\frac{5}{4}} \right\}{\text{1 unit loss}} \cr & {\text{loss}}\% = \frac{1}{5} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 20\% {\text{ loss}} \cr} $$
3. If selling price of an article is $$\frac{8}{5}$$ times of its cost price, the profit percent on it is
a) 120%
b) 160%
c) 40%
d) 60%
Explanation:
$$\eqalign{ & {\text{Selling price}} \cr & = \frac{8}{5} \times {\text{Cost price}} \cr & \frac{{{\text{Selling price}}}}{{{\text{Cost price}}}} = \left. {\frac{8}{5}} \right\}{\text{3 gain}} \cr & {\text{Gain}}\% = \frac{3}{5} \times 100 = 60\% {\text{ }} \cr} $$
4. If the cost price of 12 oranges is equal to selling price of 10 oranges, then the percentage of profit is =?
a) 16%
b) 20%
c) 18%
d) 25%
Explanation:
12 Cost Price = 10 Selling Price
$$\eqalign{ & \frac{{{\text{CP}}}}{{{\text{SP}}}} = \frac{{10}}{{12}} = \left. {\frac{5}{6}} \right\}{\text{1 profit}} \cr & {\text{Profit }}\% = \frac{1}{5} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 20\% \cr} $$
5. The cost price of an article is Rs. 7840. What should be the selling price of the article so that there is a profit of 7% ?
a) Rs. 8000
b) Rs. 8300
c) Rs. 8388.80
d) Rs. 8500
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.7840 \cr & {\text{Profit}} = 7\% \cr & \therefore {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{107}}{{100}} \times 7840} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}8388.80 \cr} $$
6. Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:
a) 30%
b) $$33\frac{1}{3}$$
c) 35%
d) 44%
Explanation:
$$\eqalign{ & {\text{Suppose,}}\,{\text{no.}}\,{\text{of}}\,{\text{articles}}\,{\text{bought}} \cr & {\text{ = }}\,{\text{L}}{\text{.C}}{\text{.M}}{\text{.}}\,{\text{of}}\,{\text{6}}\,{\text{and}}\,{\text{5 = 30}} \cr & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{30}}\,{\text{articles}} \cr & = Rs.\,\left( {\frac{5}{6} \times 30} \right) = Rs.\,25 \cr & {\text{S}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{30}}\,{\text{articles}} \cr & = Rs.\,\left( {\frac{6}{5} \times 30} \right) = Rs.\,36 \cr & \therefore {\text{Gain}}\,\% = \left( {\frac{{11}}{{25}} \times 100} \right)\% \, = 44\% \cr} $$
7. On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
a) 45
b) 50
c) 55
d) 60
Explanation:
$$\eqalign{ & {\text{(C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{17}}\,{\text{balls) - (S}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{17}}\,{\text{balls) = (C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{5}}\,{\text{balls)}} \cr & \Rightarrow {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{12}}\,{\text{balls = S}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{17}}\,{\text{balls = Rs}}{\text{.720}} \cr & \Rightarrow {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{1}}\,{\text{ball}} = Rs.\,\left( {\frac{{720}}{{12}}} \right) = Rs.\,60 \cr} $$
8. When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
a) Rs. 21,000
b) Rs. 22,500
c) Rs. 25,300
d) Rs. 25,800
Explanation:
$$\eqalign{ & 85:18700 = 115:x \cr & \Rightarrow x = {\frac{{18700 \times 115}}{{85}}} = 25300 \cr & {\text{Hence,}}\,{\text{S}}{\text{.P}}{\text{.}} = Rs.\,25300 \cr} $$
9. 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:
a) $$14\frac{2}{7}$$% gain
b) 15% gain
c) $$14\frac{2}{7}$$% loss
d) 15% loss
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{1}}\,{\text{orange}}\, \cr & = Rs.\,\left( {\frac{{350}}{{100}}} \right) = Rs.\,3.50 \cr & {\text{S}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{1}}\,{\text{orange}} \cr & = Rs.\,\left( {\frac{{48}}{{12}}} \right) = Rs.\,4 \cr & \therefore {\text{Gain}}\% = \left( {\frac{{0.50}}{{3.50}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{7}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 14\frac{2}{7}\% \cr} $$
10. A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. His total gain or loss percent is:
a) $$5\frac{{15}}{{17}}$$% loss
b) $$5\frac{{15}}{{17}}$$% gain
c) $$6\frac{2}{3}$$% gain
d) None of these
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{1^{st}}\,{\text{transistor}} \cr & = Rs.\,\left( {\frac{{100}}{{120}} \times 840} \right) = Rs.\,700 \cr & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{2^{nd}}\,{\text{transistor}} \cr & = Rs.\,\left( {\frac{{100}}{{96}} \times 960} \right) = Rs.\,1000 \cr & {\text{So,}}\,{\text{total}}\,{\text{C}}{\text{.P}}{\text{.}}\, = Rs.\,\left( {700 + 1000} \right) = Rs.\,1700 \cr & {\text{Total}}\,{\text{S}}{\text{.P}}{\text{.}}\, = \,Rs.\,\left( {840 + 960} \right) = Rs.\,1800 \cr & \therefore {\text{Gain}}\,\% = \left( {\frac{{100}}{{1700}} \times 100} \right)\% = 5\frac{{15}}{{17}}\% \cr} $$