Q1. Raman bought 10 note books for Rs.40 and sold them at Rs.4.75 per note book. Find his gain percent.
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$\Rightarrow$ C.P. of 10 note-books = 40
$\therefore$ C.P. of 1 note-books = $\dfrac{40}{10} = \text{Rs.}4$
$\Rightarrow$ S.P. of 1 note-books = Rs.$4.75$
$\Rightarrow$ Profit = $4.75 - 4.00 = 0.75$
$\therefore$ Profit% = $\dfrac{0.75}{4} \times 100$
$\Rightarrow \dfrac{75}{4 \times 100} \times 100 = \dfrac{75}{4} = 13\dfrac{3}{4}\%$ Ans
$\therefore$ C.P. of 1 note-books = $\dfrac{40}{10} = \text{Rs.}4$
$\Rightarrow$ S.P. of 1 note-books = Rs.$4.75$
$\Rightarrow$ Profit = $4.75 - 4.00 = 0.75$
$\therefore$ Profit% = $\dfrac{0.75}{4} \times 100$
$\Rightarrow \dfrac{75}{4 \times 100} \times 100 = \dfrac{75}{4} = 13\dfrac{3}{4}\%$ Ans
Q2. A fruit dealer buys apples at 4 for Rs. 3 and and sells them at 3 for Rs.4. Find profit percent.
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$\Rightarrow$ C.P. of 4 apples = Rs.3
$\therefore$ C.P. of 1 apple = $\dfrac{3}{4}$
$\Rightarrow$ S.P. of 3 apples = Rs.4
$\therefore$ S.P. of 1 apple = $\dfrac{4}{3}$
$\Rightarrow$ Profit = $\dfrac{4}{3} - \dfrac{3}{4} = \dfrac{16 - 9}{12} = \dfrac{7}{12}$
$\therefore$ Profit% = $\dfrac{\dfrac{7}{12}}{\dfrac{3}{4}} \times 100$
$\Rightarrow \dfrac{7 \times 4 \times 100}{12 \times 3} = \dfrac{700}{9} = 77\dfrac{7}{9}\%$ Ans
$\therefore$ C.P. of 1 apple = $\dfrac{3}{4}$
$\Rightarrow$ S.P. of 3 apples = Rs.4
$\therefore$ S.P. of 1 apple = $\dfrac{4}{3}$
$\Rightarrow$ Profit = $\dfrac{4}{3} - \dfrac{3}{4} = \dfrac{16 - 9}{12} = \dfrac{7}{12}$
$\therefore$ Profit% = $\dfrac{\dfrac{7}{12}}{\dfrac{3}{4}} \times 100$
$\Rightarrow \dfrac{7 \times 4 \times 100}{12 \times 3} = \dfrac{700}{9} = 77\dfrac{7}{9}\%$ Ans
Q3. A man buys a certain number of articles at 15 for Rs.112.50 and sells them at Rs. for Rs. 108. Find:
(a) Profit percent
(b) Number of articles sold to make a profit of Rs.75.
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(a) C.P. of 15 articles = Rs.112.50
$\therefore$ C.P. of 1 article = $\dfrac{112.50}{15}$
$\Rightarrow \dfrac{11250}{15 \times 100} = \dfrac{750}{100} = \dfrac{75}{10} = = \dfrac{15}{2} = \text{Rs.}7.5$
$\Rightarrow$ S.P. of 12 articles = Rs.108
$\therefore$ S.P. of 1 apple = $\dfrac{108}{12} = \text{Rs.}9$
$\Rightarrow$ Profit = $\text{Rs.}(9.0 - 7.5) = \text{Rs.}1.5$
$\therefore$ Profit% = $\dfrac{1.5}{7.5} \times 100$
$\Rightarrow \dfrac{15 \times 10}{75 \times 10} \times 100 = \dfrac{15}{75} \times 100 = \dfrac{100}{5} = 20\%$ Ans
(b) Required no. of articles sold = $\dfrac{75}{1.5} = \dfrac{75 \times 10}{15} = 5 \times 10 = 50$ Ans
$\therefore$ C.P. of 1 article = $\dfrac{112.50}{15}$
$\Rightarrow \dfrac{11250}{15 \times 100} = \dfrac{750}{100} = \dfrac{75}{10} = = \dfrac{15}{2} = \text{Rs.}7.5$
$\Rightarrow$ S.P. of 12 articles = Rs.108
$\therefore$ S.P. of 1 apple = $\dfrac{108}{12} = \text{Rs.}9$
$\Rightarrow$ Profit = $\text{Rs.}(9.0 - 7.5) = \text{Rs.}1.5$
$\therefore$ Profit% = $\dfrac{1.5}{7.5} \times 100$
$\Rightarrow \dfrac{15 \times 10}{75 \times 10} \times 100 = \dfrac{15}{75} \times 100 = \dfrac{100}{5} = 20\%$ Ans
(b) Required no. of articles sold = $\dfrac{75}{1.5} = \dfrac{75 \times 10}{15} = 5 \times 10 = 50$ Ans
Q4. A boy buys an old bicycle for Rs.162 and spends Rs.18 on its repairs. He then sells the bicycle for Rs.207; find his gain or loss percent.
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$\Rightarrow$ C.P. = Rs.162
$\Rightarrow$ Repairs = Rs.18
$\Rightarrow$ New C.P. = $162 + 18 = \text{Rs.}180$
$\Rightarrow$ Given S.P. = Rs.207
$\Rightarrow$ Profit = $207 - 180 = \text{Rs.}27$
$\therefore$ Profit% = $\dfrac{27}{180} \times 100$
$\Rightarrow \dfrac{27}{18} \times 10 = \dfrac{27}{9} \times 5 = 3 \times 5 = 15\%$ Ans
$\Rightarrow$ Repairs = Rs.18
$\Rightarrow$ New C.P. = $162 + 18 = \text{Rs.}180$
$\Rightarrow$ Given S.P. = Rs.207
$\Rightarrow$ Profit = $207 - 180 = \text{Rs.}27$
$\therefore$ Profit% = $\dfrac{27}{180} \times 100$
$\Rightarrow \dfrac{27}{18} \times 10 = \dfrac{27}{9} \times 5 = 3 \times 5 = 15\%$ Ans
Q5. An Article bought from Jaipur for Rs.4800 and is sold in Delhi for Rs.5820. If Rs.1200 is spent on its transportations etc; find his gain or loss as percent.
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$\Rightarrow$ C.P. = Rs.4800
$\Rightarrow$ Overheads = Rs.1200
$\Rightarrow$ New C.P. = $4800 + 1200 = \text{Rs.}6000$
$\Rightarrow$ Given, S.P. = Rs.5800
$\therefore$ Loss = $6000 - 5800 = \text{Rs.}200$
$\Rightarrow$ Loss% = $\dfrac{200}{6000} \times 100$
$\Rightarrow \dfrac{2}{60} \times 100 = \dfrac{2}{6} \times 10 = \dfrac{10}{3} = 3\dfrac{1}{3}$ Ans.
$\Rightarrow$ Overheads = Rs.1200
$\Rightarrow$ New C.P. = $4800 + 1200 = \text{Rs.}6000$
$\Rightarrow$ Given, S.P. = Rs.5800
$\therefore$ Loss = $6000 - 5800 = \text{Rs.}200$
$\Rightarrow$ Loss% = $\dfrac{200}{6000} \times 100$
$\Rightarrow \dfrac{2}{60} \times 100 = \dfrac{2}{6} \times 10 = \dfrac{10}{3} = 3\dfrac{1}{3}$ Ans.
Q6. Rajan sold a TV for Rs. 3600; gaining one-sixth of its selling price. Find:
(a) Profit
(b) C.P. of TV
(c) Profit percent
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$\Rightarrow$ Given, S.P. = Rs.3600
(a) Profit = $\dfrac{1}{6} \times 3600 = 600$ Ans
(b) C.P. = $3600 - 600 = \text{Rs.}3000$ Ans
(c) Profit% = $\dfrac{600}{3000} \times 100 = \dfrac{100}{5} = 20\%$ Ans
(a) Profit = $\dfrac{1}{6} \times 3600 = 600$ Ans
(b) C.P. = $3600 - 600 = \text{Rs.}3000$ Ans
(c) Profit% = $\dfrac{600}{3000} \times 100 = \dfrac{100}{5} = 20\%$ Ans
Q7. By selling a certain number of goods for Rs. 5500, a shopkeeper losses equal to $\dfrac{1}{10}$ of their selling price/ Find:
(a) Loss incured
(b) C.P. of goods
(c) Loss percent
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$\Rightarrow$ Given, S.P. = Rs.5500
(a) Loss = $\dfrac{1}{10} \times 5500 = 550$ Ans
(b) C.P. = $5500 - 550 = \text{Rs.}6050$ Ans
(c) Loss% = $\dfrac{550}{6050} \times 100 = \dfrac{100}{11} = 9\dfrac{1}{11}\%$ Ans
(a) Loss = $\dfrac{1}{10} \times 5500 = 550$ Ans
(b) C.P. = $5500 - 550 = \text{Rs.}6050$ Ans
(c) Loss% = $\dfrac{550}{6050} \times 100 = \dfrac{100}{11} = 9\dfrac{1}{11}\%$ Ans
Q8. The selling price of a sofa-set is $\dfrac{4}{5}$ times of its cost price. Find the gain or loss percent.
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$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. = $\dfrac{4}{5} \times 100 = \text{Rs.}80$
$\Rightarrow$ Loss = $100 - 80 = \text{Rs.}20$
$\therefore$ Loss% = $\dfrac{20}{100} \times 100 = 20\%$ Ans.
$\therefore$ S.P. = $\dfrac{4}{5} \times 100 = \text{Rs.}80$
$\Rightarrow$ Loss = $100 - 80 = \text{Rs.}20$
$\therefore$ Loss% = $\dfrac{20}{100} \times 100 = 20\%$ Ans.
Q9. The cost price of a sofa-set is $\dfrac{4}{5}$ times of its selling price. Find the gain or loss percent.
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$\Rightarrow$ Let S.P. be = Rs.100
$\therefore$ C.P. = $\dfrac{4}{5} \times 100 = \text{Rs.}80$
$\Rightarrow$ Profit = $100 - 80 = \text{Rs.}20$
$\therefore$ Profit% = $\dfrac{20}{80} \times 100 = \dfrac{100}{4} = 25\%$ Ans.
$\therefore$ C.P. = $\dfrac{4}{5} \times 100 = \text{Rs.}80$
$\Rightarrow$ Profit = $100 - 80 = \text{Rs.}20$
$\therefore$ Profit% = $\dfrac{20}{80} \times 100 = \dfrac{100}{4} = 25\%$ Ans.
Q10. A shopkeeper sells his goods at $80\%$ of their cost price. Find his gain or loss percent.
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$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. = $\dfrac{80}{100} \times 100 = \text{Rs.}80$
$\Rightarrow$ Loss = $100 - 80 = \text{Rs.}20$
$\therefore$ Loss% = $\dfrac{20}{100} \times 100 = 20\%$ Ans.
$\therefore$ S.P. = $\dfrac{80}{100} \times 100 = \text{Rs.}80$
$\Rightarrow$ Loss = $100 - 80 = \text{Rs.}20$
$\therefore$ Loss% = $\dfrac{20}{100} \times 100 = 20\%$ Ans.
Q11. The cost price of an article is $90\%$ of its selling price. Find profit or loss as percent.
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$\Rightarrow$ Let S.P. be = Rs.100
$\therefore$ C.P. = $\dfrac{90}{100} \times 100 = \text{Rs.}90$
$\Rightarrow$ Profit = $100 - 90 = \text{Rs.}10$
$\therefore$ Profit% = $\dfrac{10}{90} \times 100 = \dfrac{100}{9} = 11\dfrac{1}{9}\%$ Ans.
$\therefore$ C.P. = $\dfrac{90}{100} \times 100 = \text{Rs.}90$
$\Rightarrow$ Profit = $100 - 90 = \text{Rs.}10$
$\therefore$ Profit% = $\dfrac{10}{90} \times 100 = \dfrac{100}{9} = 11\dfrac{1}{9}\%$ Ans.
Q12. The cost price of an article is $30\%$ less than its selling price. Find gain or loss percent.
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$\Rightarrow$ Let S.P. be = Rs.100
$\therefore$ C.P. = $100 - \dfrac{30}{100} \times 100 = 100 - 30 = \text{Rs.}70$
$\Rightarrow$ Profit = $100 - 70 = \text{Rs.}30$
$\therefore$ Profit% = $\dfrac{30}{70} \times 100 = \dfrac{300}{7} = 42\dfrac{6}{7}\%$ Ans.
$\therefore$ C.P. = $100 - \dfrac{30}{100} \times 100 = 100 - 30 = \text{Rs.}70$
$\Rightarrow$ Profit = $100 - 70 = \text{Rs.}30$
$\therefore$ Profit% = $\dfrac{30}{70} \times 100 = \dfrac{300}{7} = 42\dfrac{6}{7}\%$ Ans.
Q13. A shopkeeper buys 300 apples at 80 paise each. After purchase, he found 30 apples to be rotten. He sold the remaining apples at Rs.1 each. Find gain or loss percent.
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$\Rightarrow$ Total no. of apples = 300
$\Rightarrow$ No. of rotten apples = 30
$\Rightarrow$ Remaining no. of apples = $300 - 30 = 270$
$\Rightarrow$ Given, C.P. of 1 apple = 80 paise or Rs.0.80
$\therefore$ C.P. of 300 apples = $300 \times 0.80 = \text{Rs.}240$
$\Rightarrow$ Given, S.P. of 1 apple = Rs.1
$\therefore$ S.P. of 240 apples = $240 \times 1 = \text{Rs.}240$
$\Rightarrow$ Profit = $270 - 240 = \text{Rs.}30$
$\therefore$ Profit% = $\dfrac{30}{240} \times 100 = \dfrac{100}{8} = \dfrac{25}{2} = 12\dfrac{1}{2}\%$ Ans.
$\Rightarrow$ No. of rotten apples = 30
$\Rightarrow$ Remaining no. of apples = $300 - 30 = 270$
$\Rightarrow$ Given, C.P. of 1 apple = 80 paise or Rs.0.80
$\therefore$ C.P. of 300 apples = $300 \times 0.80 = \text{Rs.}240$
$\Rightarrow$ Given, S.P. of 1 apple = Rs.1
$\therefore$ S.P. of 240 apples = $240 \times 1 = \text{Rs.}240$
$\Rightarrow$ Profit = $270 - 240 = \text{Rs.}30$
$\therefore$ Profit% = $\dfrac{30}{240} \times 100 = \dfrac{100}{8} = \dfrac{25}{2} = 12\dfrac{1}{2}\%$ Ans.
Q14. A man sold his bicycle for Rs.405 losing $\dfrac{1}{10}$ of its cost price. Find:
(a) Cost Price
(b) Loss percent
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(a) Given S.P. = Rs.405
$\Rightarrow$ Let C.P. be = Rs.$x$
$\Rightarrow$ Given loss = $x - x \times \dfrac{1}{10}$
$\Rightarrow x - \dfrac{x}{10} = \dfrac{10x - x}{10} = \dfrac{9x}{10}$
$\therefore \dfrac{9x}{10} = 405$
$\Rightarrow 9x = 405 \times 10$
$\Rightarrow x = \dfrac{405 \times 10}{9} = 45 \times 10 = \text{Rs.}450$
So, we have C.P. = Rs.450 Ans
(b) Loss = $450 - 405 = \text{Rs.}45$
$\therefore$ Loss% = $\dfrac{45}{450} \times 100 = \dfrac{100}{10} = 10\%$ Ans
$\Rightarrow$ Let C.P. be = Rs.$x$
$\Rightarrow$ Given loss = $x - x \times \dfrac{1}{10}$
$\Rightarrow x - \dfrac{x}{10} = \dfrac{10x - x}{10} = \dfrac{9x}{10}$
$\therefore \dfrac{9x}{10} = 405$
$\Rightarrow 9x = 405 \times 10$
$\Rightarrow x = \dfrac{405 \times 10}{9} = 45 \times 10 = \text{Rs.}450$
So, we have C.P. = Rs.450 Ans
(b) Loss = $450 - 405 = \text{Rs.}45$
$\therefore$ Loss% = $\dfrac{45}{450} \times 100 = \dfrac{100}{10} = 10\%$ Ans
Q15. A man sold a transistor for Rs.250 gaining $\dfrac{1}{9}$ of its cost price. Find:
(a) Cost Price
(b) Profit percent
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(a) Given S.P. = Rs.250
$\Rightarrow$ Let C.P. be = Rs.$x$
$\Rightarrow$ Given profit = $x + x \times \dfrac{1}{9}$
$\Rightarrow x + \dfrac{x}{9} = \dfrac{9x + x}{9} = \dfrac{10x}{9}$
$\therefore \dfrac{10x}{9} = 250$
$\Rightarrow 10x = 250 \times 9$
$\Rightarrow x = \dfrac{250 \times 9}{10} = 25 \times 9 = \text{Rs.}225$
So, we have C.P. = Rs.225 Ans
(b) Profit = $250 - 225 = \text{Rs.}25$
$\therefore$ Profit% = $\dfrac{25}{225} \times 100 = \dfrac{100}{9} = 11\dfrac{1}{9}\%$ Ans
$\Rightarrow$ Let C.P. be = Rs.$x$
$\Rightarrow$ Given profit = $x + x \times \dfrac{1}{9}$
$\Rightarrow x + \dfrac{x}{9} = \dfrac{9x + x}{9} = \dfrac{10x}{9}$
$\therefore \dfrac{10x}{9} = 250$
$\Rightarrow 10x = 250 \times 9$
$\Rightarrow x = \dfrac{250 \times 9}{10} = 25 \times 9 = \text{Rs.}225$
So, we have C.P. = Rs.225 Ans
(b) Profit = $250 - 225 = \text{Rs.}25$
$\therefore$ Profit% = $\dfrac{25}{225} \times 100 = \dfrac{100}{9} = 11\dfrac{1}{9}\%$ Ans