Q16. If Raman sells his bicycle for Rs.637, he suffers a loss of $9\%$. For how much should he sell it, if he desires a profit of $5\%$.
Show Answer
$\Rightarrow$ Given, S.P. = Rs.637
$\Rightarrow$ Given, Loss% = 9%
$\Rightarrow$ Let C.P. be = Rs.100
$\Rightarrow$ S.P. = $100 - \dfrac{9}{100} \times 100 = 100 - 9 = \text{Rs.}91$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 637}{91} = 100 \times 7 = \text{Rs.}700$
$\therefore$ Required S.P. = $700 + \dfrac{5}{100} \times 700$
$\Rightarrow 700 + 5 \times 7 = 700 + 35 = \text{Rs.}735$ Ans
$\Rightarrow$ Given, Loss% = 9%
$\Rightarrow$ Let C.P. be = Rs.100
$\Rightarrow$ S.P. = $100 - \dfrac{9}{100} \times 100 = 100 - 9 = \text{Rs.}91$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 637}{91} = 100 \times 7 = \text{Rs.}700$
$\therefore$ Required S.P. = $700 + \dfrac{5}{100} \times 700$
$\Rightarrow 700 + 5 \times 7 = 700 + 35 = \text{Rs.}735$ Ans
Q17. A man sells his radio set for Rs.605 making a profit of $10\%$. At what price should he sell another similar radio in order to gain $16\%$.
Show Answer
$\Rightarrow$ Given, S.P. = Rs.605
$\Rightarrow$ Given, Profit% = 10\%
$\Rightarrow$ Let C.P. be = Rs.100
$\Rightarrow$ S.P. = $100 + \dfrac{10}{100} \times 100 = 100 + 10 = \text{Rs.}110$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 605}{110} = 10 \times 55 = \text{Rs.}550$
$\therefore$ Required S.P. = $550 + \dfrac{16}{100} \times 550$
$\Rightarrow 550 + \dfrac{16}{10} \times 55 = 550 + \dfrac{16}{2} \times 11 = 550 + 8 \times 11 = 550 + 88 = \text{Rs.}638$ Ans
$\Rightarrow$ Given, Profit% = 10\%
$\Rightarrow$ Let C.P. be = Rs.100
$\Rightarrow$ S.P. = $100 + \dfrac{10}{100} \times 100 = 100 + 10 = \text{Rs.}110$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 605}{110} = 10 \times 55 = \text{Rs.}550$
$\therefore$ Required S.P. = $550 + \dfrac{16}{100} \times 550$
$\Rightarrow 550 + \dfrac{16}{10} \times 55 = 550 + \dfrac{16}{2} \times 11 = 550 + 8 \times 11 = 550 + 88 = \text{Rs.}638$ Ans
Q18. By selling a UPS for Rs.2500 the shopkeeper loses $20\%$. Find his gain percent if he had sold the UPS for Rs.3150.
Show Answer
$\Rightarrow$ Given, S.P. = Rs.2500
$\Rightarrow$ Given, Profit% = 20\%
$\Rightarrow$ Let C.P. be = Rs.100
$\Rightarrow$ S.P. = $100 - \dfrac{20}{100} \times 100 = 100 - 20 = \text{Rs.}80$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 2500}{80} = \dfrac{10 \times 2500}{8} = \dfrac{5 \times 2500}{4} = 5 \times 625 = \text{Rs.}3125$
$\Rightarrow$ Profit on selling the S.P. at new C.P. = $3150 - 3125 = $Rs.25
$\therefore$ Profit% = $\dfrac{25}{3125} \times 100$
$\Rightarrow \dfrac{100}{125} = \dfrac{4}{5} = 0.8\%$ Ans
$\Rightarrow$ Given, Profit% = 20\%
$\Rightarrow$ Let C.P. be = Rs.100
$\Rightarrow$ S.P. = $100 - \dfrac{20}{100} \times 100 = 100 - 20 = \text{Rs.}80$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 2500}{80} = \dfrac{10 \times 2500}{8} = \dfrac{5 \times 2500}{4} = 5 \times 625 = \text{Rs.}3125$
$\Rightarrow$ Profit on selling the S.P. at new C.P. = $3150 - 3125 = $Rs.25
$\therefore$ Profit% = $\dfrac{25}{3125} \times 100$
$\Rightarrow \dfrac{100}{125} = \dfrac{4}{5} = 0.8\%$ Ans
Q19. Yogesh sold two memory cards for Rs.990 each making $10\%$ profit on one and losing $10\%$ on another. Find his total gain or loss percent.
Show Answer
$\Rightarrow$ S.P. for $1^{st}$ memory card = Rs.990
$\Rightarrow$ Profit% = 10\%
$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. = $100 + \dfrac{10}{100} \times 100 = 100 + 10 = \text{Rs.}110$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 990}{110} = 100 \times 9 = \text{Rs.}900$
$\Rightarrow$ S.P. for $2^{nd}$ memory card = Rs.990
$\Rightarrow$ Loss% = 10\%
$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. = $100 - \dfrac{10}{100} \times 100 = 100 - 10 = \text{Rs.}90$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 990}{90} = 100 \times 11 = \text{Rs.}1100$
$\therefore$ Total C.P. = $1100 + 900 = \text{Rs.}2000$
$\Rightarrow$ Total S.P. = $990 + 990 = \text{Rs.}1980$
$\Rightarrow$ Loss = $2000 - 1980 = \text{Rs.}20$
$\therefore \dfrac{20}{2000} \times 100 = 1\%$ Ans
$\Rightarrow$ Profit% = 10\%
$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. = $100 + \dfrac{10}{100} \times 100 = 100 + 10 = \text{Rs.}110$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 990}{110} = 100 \times 9 = \text{Rs.}900$
$\Rightarrow$ S.P. for $2^{nd}$ memory card = Rs.990
$\Rightarrow$ Loss% = 10\%
$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. = $100 - \dfrac{10}{100} \times 100 = 100 - 10 = \text{Rs.}90$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 990}{90} = 100 \times 11 = \text{Rs.}1100$
$\therefore$ Total C.P. = $1100 + 900 = \text{Rs.}2000$
$\Rightarrow$ Total S.P. = $990 + 990 = \text{Rs.}1980$
$\Rightarrow$ Loss = $2000 - 1980 = \text{Rs.}20$
$\therefore \dfrac{20}{2000} \times 100 = 1\%$ Ans
Q20. A C.D. player is sold for Rs.2760 at a gain of $15\%$ and a speaker is sold for Rs.3240 at a loss of $10\%$. Find:
(i) C.P. of C.D. player
(ii) C.P. of speaker
(iii) Combined cost price
(iv) Combined selling price
(v) Gain or Loss percent
Show Answer
(i) S.P. of C.D. player = Rs.2760
$\Rightarrow$ Profit% = 15\%
$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. = $100 + \dfrac{15}{100} \times 100 = 100 + 15 = \text{Rs.}115$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 2760}{115} = 20 \times 120 = \text{Rs.}2400$ Ans
(ii) S.P. for Speaker = Rs.3240
$\Rightarrow$ Loss% = 10\%
$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. = $100 - \dfrac{10}{100} \times 100 = 100 - 10 = \text{Rs.}90$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 3240}{90} = 100 \times 36 = \text{Rs.}3600$ Ans
(iii) Total C.P. = $2400 + 3600 = 6000$ Ans
(iv) Total S.P. = $2760 + 3240 = 6000$ Ans
(v) The C.P. and S.P. being the same; there is neither profit nor loss. Ans
$\Rightarrow$ Profit% = 15\%
$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. = $100 + \dfrac{15}{100} \times 100 = 100 + 15 = \text{Rs.}115$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 2760}{115} = 20 \times 120 = \text{Rs.}2400$ Ans
(ii) S.P. for Speaker = Rs.3240
$\Rightarrow$ Loss% = 10\%
$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. = $100 - \dfrac{10}{100} \times 100 = 100 - 10 = \text{Rs.}90$
$\Rightarrow$ Actual C.P. = $\dfrac{100 \times 3240}{90} = 100 \times 36 = \text{Rs.}3600$ Ans
(iii) Total C.P. = $2400 + 3600 = 6000$ Ans
(iv) Total S.P. = $2760 + 3240 = 6000$ Ans
(v) The C.P. and S.P. being the same; there is neither profit nor loss. Ans
Q21. Ramesh sold his scooter to Rajesh at $8\%$ loss. Rajesh sold the same scooter to Raman at $5\%$. If Raman paid Rs.14,490 for the scooter, find:
(a) S.P. and C.P. of scooter to Rajesh
(b) S.P. and C.P. of scooter to Ramesh
Show Answer
(a) $\because$ Raman paid Rs.14,490 to Rajesh
$\therefore$ S.P. for Rajesh = Rs.14,490 Ans
$\Rightarrow$ Given, Profit% = 5\%
$\Rightarrow$ Let C.P. for Rajesh be = Rs.100
$\Rightarrow$ S.P. for Rajesh = $100 + \dfrac{5}{100} \times 100$
$\Rightarrow 100 + 5 = \text{Rs.}105$
$\therefore$ When S.P. is Rs.105, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{105}$
$\Rightarrow$ When S.P. is Rs.14,490, then C.P. = $\dfrac{100}{105} \times 14,490$
$\Rightarrow 100 \times 138 = \text{Rs.}13,800$ Ans
(b) $\because$ C.P. for Rajesh = S.P. for Ramesh
$\therefore$ S.P. for Ramesh = Rs.13,800
$\Rightarrow$ Given Loss% = 8\%
$\Rightarrow$ Let C.P. for Ramesh be = Rs.100
$\Rightarrow$ S.P. for Rajesh = $100 + \dfrac{8}{100} \times 100$
$\Rightarrow 100 - 8 = \text{Rs.}92$
$\therefore$ When S.P. is Rs.92, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{92}$
$\Rightarrow$ When S.P. is Rs.14,490, then C.P. = $\dfrac{100}{92} \times 13,800$
$\Rightarrow 100 \times 150 = \text{Rs.}15,000$ Ans
$\therefore$ S.P. for Rajesh = Rs.14,490 Ans
$\Rightarrow$ Given, Profit% = 5\%
$\Rightarrow$ Let C.P. for Rajesh be = Rs.100
$\Rightarrow$ S.P. for Rajesh = $100 + \dfrac{5}{100} \times 100$
$\Rightarrow 100 + 5 = \text{Rs.}105$
$\therefore$ When S.P. is Rs.105, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{105}$
$\Rightarrow$ When S.P. is Rs.14,490, then C.P. = $\dfrac{100}{105} \times 14,490$
$\Rightarrow 100 \times 138 = \text{Rs.}13,800$ Ans
(b) $\because$ C.P. for Rajesh = S.P. for Ramesh
$\therefore$ S.P. for Ramesh = Rs.13,800
$\Rightarrow$ Given Loss% = 8\%
$\Rightarrow$ Let C.P. for Ramesh be = Rs.100
$\Rightarrow$ S.P. for Rajesh = $100 + \dfrac{8}{100} \times 100$
$\Rightarrow 100 - 8 = \text{Rs.}92$
$\therefore$ When S.P. is Rs.92, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{92}$
$\Rightarrow$ When S.P. is Rs.14,490, then C.P. = $\dfrac{100}{92} \times 13,800$
$\Rightarrow 100 \times 150 = \text{Rs.}15,000$ Ans
Q22. Peter sold an article to John at $20\%$ gain percent and Peter sold it to Mohan at $5\%$. If Mohan paid Rs.912 for the article, find C.P. for John?
Show Answer
$\Rightarrow$ S.P. for John = Rs.912
$\Rightarrow$ Given Loss% = 5%
$\Rightarrow$ Let C.P. for John be = Rs.100
$\therefore$ S.P. for John be = $100 - \dfrac{5}{100} \times 100$
$\Rightarrow 100 - 5 = \text{Rs.}95$
$\therefore$ When S.P. is Rs.95, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{95}$
$\Rightarrow$ When S.P. is Rs.192, then C.P. = $\dfrac{100}{95} \times 912$
$\Rightarrow \dfrac{20}{19} \times 912 = 20 \times 48 = \text{Rs.}960$
$\because$ C.P. for John = S.P. for Peter
$\therefore$ S.P. for Peter = Rs.960
$\Rightarrow$ Given, Profit% = 20%
$\Rightarrow$ Let C.P. for Peter be = Rs.100
$\therefore$ S.P. for Peter = $100 + \dfrac{20}{100} \times 100$
$\Rightarrow 100 + 20 = \text{Rs.}120$
$\therefore$ When S.P. is Rs.120, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{120}$
$\Rightarrow$ When S.P. is Rs.960, then C.P. = $\dfrac{100}{120} \times 960$
$\Rightarrow 100 \times 8 = \text{Rs.}800$ Ans
$\Rightarrow$ Given Loss% = 5%
$\Rightarrow$ Let C.P. for John be = Rs.100
$\therefore$ S.P. for John be = $100 - \dfrac{5}{100} \times 100$
$\Rightarrow 100 - 5 = \text{Rs.}95$
$\therefore$ When S.P. is Rs.95, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{95}$
$\Rightarrow$ When S.P. is Rs.192, then C.P. = $\dfrac{100}{95} \times 912$
$\Rightarrow \dfrac{20}{19} \times 912 = 20 \times 48 = \text{Rs.}960$
$\because$ C.P. for John = S.P. for Peter
$\therefore$ S.P. for Peter = Rs.960
$\Rightarrow$ Given, Profit% = 20%
$\Rightarrow$ Let C.P. for Peter be = Rs.100
$\therefore$ S.P. for Peter = $100 + \dfrac{20}{100} \times 100$
$\Rightarrow 100 + 20 = \text{Rs.}120$
$\therefore$ When S.P. is Rs.120, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{120}$
$\Rightarrow$ When S.P. is Rs.960, then C.P. = $\dfrac{100}{120} \times 960$
$\Rightarrow 100 \times 8 = \text{Rs.}800$ Ans
Q23. A man sells 12 articles for Rs.80 gaining $33\dfrac{1}{3}\%$. Find number of articles bought at Rs.90.
Show Answer
$\Rightarrow$ Let C.P. of 12 articles be = Rs.100
$\Rightarrow$ Given Profit% = $33\dfrac{1}{3}\% = \dfrac{100}{3}\%$
$\therefore$ S.P. 12 articles = $100 + \dfrac{100}{3 \times 100} \times 100$
$\Rightarrow 100 + \dfrac{100}{3} = \dfrac{300 + 100}{3} = \text{Rs.}\dfrac{400}{3}$
$\Rightarrow$ Given, S.P. = Rs.80
$\therefore$ When S.P. is $\text{Rs.}\dfrac{400}{3}$, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{\dfrac{400}{3}} = \dfrac{100 \times 3}{400}$
$\Rightarrow$ When S.P. is Rs.80, then C.P. = $\dfrac{100 \times 3 \times 80}{400}$
$\Rightarrow \dfrac{3 \times 80}{4} = 3 \times 20 = \text{Rs.}60$
$\Rightarrow$ Now, C.P. for 12 articles = Rs.60
$\Rightarrow$ C.P. for 1 article = $\dfrac{60}{12} = \text{Rs.}5$
$\therefore$ No. of articles bought for Rs.90 = $\dfrac{90}{5} = 18$ Ans
$\Rightarrow$ Given Profit% = $33\dfrac{1}{3}\% = \dfrac{100}{3}\%$
$\therefore$ S.P. 12 articles = $100 + \dfrac{100}{3 \times 100} \times 100$
$\Rightarrow 100 + \dfrac{100}{3} = \dfrac{300 + 100}{3} = \text{Rs.}\dfrac{400}{3}$
$\Rightarrow$ Given, S.P. = Rs.80
$\therefore$ When S.P. is $\text{Rs.}\dfrac{400}{3}$, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{\dfrac{400}{3}} = \dfrac{100 \times 3}{400}$
$\Rightarrow$ When S.P. is Rs.80, then C.P. = $\dfrac{100 \times 3 \times 80}{400}$
$\Rightarrow \dfrac{3 \times 80}{4} = 3 \times 20 = \text{Rs.}60$
$\Rightarrow$ Now, C.P. for 12 articles = Rs.60
$\Rightarrow$ C.P. for 1 article = $\dfrac{60}{12} = \text{Rs.}5$
$\therefore$ No. of articles bought for Rs.90 = $\dfrac{90}{5} = 18$ Ans
Q24. A rice dealer bought rice for Rs.4500/ He sold $\dfrac{1}{3}$ of it at $10\%$. If he desires to make a profit of $12\%$ on the whole, find:
(a) S.P. of remaining rice
(b) Gain percent on remaining rice
Show Answer
(a) C.P. of rice = Rs.4500
$\Rightarrow$ C.P. of $\dfrac{1}{3}$ of rice = $\dfrac{1}{3} \times 4500 = \text{Rs.}1500$
$\Rightarrow$ C.P. of remaining rice = $4500 - 1500 = \text{Rs.}3000$
$\Rightarrow$ At 10\% profit S.P. of remaining rice = $1500 + \dfrac{10}{1500} \times 1500$
$\Rightarrow 1500 + 10 \times 15 = 1500 + 150 = \text{Rs.}1650$
$\Rightarrow$ S.P. of whole rice at 12\% profit = $4500 + \dfrac{12}{100} \times 4500$
$\Rightarrow 4500 + 12 \times 45 = 4500 + 540 = \text{Rs.}5040$
$\Rightarrow$ S.P. of remaining rice = $5040 - 1650 = \text{Rs.}3390$ Ans
(b) Profit on remaining rice = $3390 - 3000 = 390$
$\therefore$ Profit% = $\dfrac{390}{3000} \times 100$
$\Rightarrow \dfrac{39}{3} = 13\%$ Ans
$\Rightarrow$ C.P. of $\dfrac{1}{3}$ of rice = $\dfrac{1}{3} \times 4500 = \text{Rs.}1500$
$\Rightarrow$ C.P. of remaining rice = $4500 - 1500 = \text{Rs.}3000$
$\Rightarrow$ At 10\% profit S.P. of remaining rice = $1500 + \dfrac{10}{1500} \times 1500$
$\Rightarrow 1500 + 10 \times 15 = 1500 + 150 = \text{Rs.}1650$
$\Rightarrow$ S.P. of whole rice at 12\% profit = $4500 + \dfrac{12}{100} \times 4500$
$\Rightarrow 4500 + 12 \times 45 = 4500 + 540 = \text{Rs.}5040$
$\Rightarrow$ S.P. of remaining rice = $5040 - 1650 = \text{Rs.}3390$ Ans
(b) Profit on remaining rice = $3390 - 3000 = 390$
$\therefore$ Profit% = $\dfrac{390}{3000} \times 100$
$\Rightarrow \dfrac{39}{3} = 13\%$ Ans
Q25. Suresh bought a certian number of note books for Rs.600. He sold $\dfrac{1}{4}$ of them at 5\% loss. At what price should he sell remaining note books for gaining 10\% on the whole.
Show Answer
$\Rightarrow$ C.P. of note-books = Rs.600
$\Rightarrow$ C.P. of $\dfrac{1}{4}$ of note-books = $\dfrac{1}{4} \times 600 = \text{Rs.}150$
$\Rightarrow$ S.P. of $\dfrac{1}{4}$ of note-books at 5\% loss = $150 - \dfrac{5}{100} \times 150$
$\Rightarrow 150 - \dfrac{5}{10} \times 15 = 150 - \dfrac{15}{2} = 150 - 7.5 = \text{Rs.}142.50$
$\Rightarrow$ S.P. of whole note-books at 10\% profit = $600 + \dfrac{10}{100} \times 600$
$\Rightarrow 600 + 60 = \text{Rs.}660$
$\therefore$ Rerquired S.P. of remaining note-books = $660 - 142.50 = \text{Rs.}517.50$ Ans
$\Rightarrow$ C.P. of $\dfrac{1}{4}$ of note-books = $\dfrac{1}{4} \times 600 = \text{Rs.}150$
$\Rightarrow$ S.P. of $\dfrac{1}{4}$ of note-books at 5\% loss = $150 - \dfrac{5}{100} \times 150$
$\Rightarrow 150 - \dfrac{5}{10} \times 15 = 150 - \dfrac{15}{2} = 150 - 7.5 = \text{Rs.}142.50$
$\Rightarrow$ S.P. of whole note-books at 10\% profit = $600 + \dfrac{10}{100} \times 600$
$\Rightarrow 600 + 60 = \text{Rs.}660$
$\therefore$ Rerquired S.P. of remaining note-books = $660 - 142.50 = \text{Rs.}517.50$ Ans
Q26. Vinod sells a watch at $5\%$ profit. Had he sold for Rs.24 more, he would have gained $11\%$. Find C.P. of watch.
Show Answer
$\Rightarrow$ Let C.P. be = Rs.100
$\because$ S.P. at 5\% profit = $100 + \dfrac{5}{100} \times 100$
$\Rightarrow 100 + 5 = \text{Rs.}105$
$\therefore$ S.P. at 11\% profit = $100 + \dfrac{11}{100} \times 100$
$\Rightarrow 100 + 11 = \text{Rs.}111$
$\Rightarrow$ As such, difference = $111 - 105 = \text{Rs.}6$
$\therefore$ When difference is Rs.6, then C.P. = 100
$\Rightarrow$ When difference is Rs.1, then C.P. = $\dfrac{100}{6}$
$\Rightarrow$ When difference is Rs.24, then C.P. = $\dfrac{100}{6} \times 24$
$\Rightarrow 100 \times 4 = \text{Rs.}400$ Ans
$\because$ S.P. at 5\% profit = $100 + \dfrac{5}{100} \times 100$
$\Rightarrow 100 + 5 = \text{Rs.}105$
$\therefore$ S.P. at 11\% profit = $100 + \dfrac{11}{100} \times 100$
$\Rightarrow 100 + 11 = \text{Rs.}111$
$\Rightarrow$ As such, difference = $111 - 105 = \text{Rs.}6$
$\therefore$ When difference is Rs.6, then C.P. = 100
$\Rightarrow$ When difference is Rs.1, then C.P. = $\dfrac{100}{6}$
$\Rightarrow$ When difference is Rs.24, then C.P. = $\dfrac{100}{6} \times 24$
$\Rightarrow 100 \times 4 = \text{Rs.}400$ Ans
Q27. A bicycle was sold at $5\%$ profit. If he cost had been $30\%$ less and the selling price Rs.63 less, he would have made a profit of $30\%$. Find C.P. of bicycle.
Show Answer
$\Rightarrow$ Let C.P. be = Rs.100
$\therefore$ S.P. at 5\% profit = $100 + \dfrac{5}{100} \times 100$
$\Rightarrow 100 + 5 = \text{Rs.}105$
$\because$ C.P. at 30\% loss = $100 - \dfrac{30}{100} \times 100$
$\Rightarrow 100 - 30 = \text{Rs.}70$
$\therefore$ S.P. at 30\% profit = $70 + \dfrac{30}{100} \times 70$
$\Rightarrow 70 + 7 \times 3 = 70 + 21 = \text{Rs.}91$
$\therefore$ Difference = $105 - 91 = \text{Rs.}14$
$\therefore$ When difference is Rs.14, then C.P. = 100
$\Rightarrow$ When difference is Rs.1, then C.P. = $\dfrac{100}{14}$
$\Rightarrow$ When difference is Rs.63, then C.P. = $\dfrac{100}{14} \times 63$
$\Rightarrow \dfrac{50}{7} \times 63 = 50 \times 9 = \text{Rs.}450$ Ans
$\therefore$ S.P. at 5\% profit = $100 + \dfrac{5}{100} \times 100$
$\Rightarrow 100 + 5 = \text{Rs.}105$
$\because$ C.P. at 30\% loss = $100 - \dfrac{30}{100} \times 100$
$\Rightarrow 100 - 30 = \text{Rs.}70$
$\therefore$ S.P. at 30\% profit = $70 + \dfrac{30}{100} \times 70$
$\Rightarrow 70 + 7 \times 3 = 70 + 21 = \text{Rs.}91$
$\therefore$ Difference = $105 - 91 = \text{Rs.}14$
$\therefore$ When difference is Rs.14, then C.P. = 100
$\Rightarrow$ When difference is Rs.1, then C.P. = $\dfrac{100}{14}$
$\Rightarrow$ When difference is Rs.63, then C.P. = $\dfrac{100}{14} \times 63$
$\Rightarrow \dfrac{50}{7} \times 63 = 50 \times 9 = \text{Rs.}450$ Ans
Q28. A shopkeeper makes a profit of $20\%$ on selling a radio for Rs.840. For how much should he sell another radio, whose C.P. is Rs.25 more than the first in order to make the same profit percent.
Show Answer
$\Rightarrow$ Let C.P. of radio be = Rs.100
$\therefore$ S.P. of radio = $100 + \dfrac{20}{100} \times 100 = 100 + 20 = \text{Rs.}120$
$\therefore$ When S.P. is Rs.120, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{120}$
$\Rightarrow$ When S.P. is Rs.840, then C.P. = $\dfrac{100}{120} \times 840$
$\Rightarrow \dfrac{100}{120} \times 840 = 100 \times 7 = \text{Rs.}700$
$\Rightarrow$ Now, C.P. of $2^{nd}$ radio = $700 + 25 = \text{Rs.}725$
$\Rightarrow$ Required profit = $\dfrac{20}{100} \times 725 = \dfrac{725}{5} = \text{Rs.}145$
$\therefore$ S.P. of $2^{nd}$ radio = $725 + 145 = \text{Rs.}870$ Ans
$\therefore$ S.P. of radio = $100 + \dfrac{20}{100} \times 100 = 100 + 20 = \text{Rs.}120$
$\therefore$ When S.P. is Rs.120, then C.P. = 100
$\Rightarrow$ When S.P. is Rs.1, then C.P. = $\dfrac{100}{120}$
$\Rightarrow$ When S.P. is Rs.840, then C.P. = $\dfrac{100}{120} \times 840$
$\Rightarrow \dfrac{100}{120} \times 840 = 100 \times 7 = \text{Rs.}700$
$\Rightarrow$ Now, C.P. of $2^{nd}$ radio = $700 + 25 = \text{Rs.}725$
$\Rightarrow$ Required profit = $\dfrac{20}{100} \times 725 = \dfrac{725}{5} = \text{Rs.}145$
$\therefore$ S.P. of $2^{nd}$ radio = $725 + 145 = \text{Rs.}870$ Ans
Q29. The cost of manufacturing an article is made up of material, labour and overheads in the ratio $4:3:2$. If the cost of labour is Rs.45, find the total cost of article. Also, find the profit percent if the article is sold for Rs.180.
Show Answer
$\Rightarrow$ Given ratio = $4 : 3 : 2$
$\Rightarrow$ Let cost of labour be = Rs.$3x$
$\therefore$ Cost of labour = $3x = 45$
$\Rightarrow x = \dfrac{45}{3} = \text{Rs.}15$
$\Rightarrow$ Sum of ratio = $ 4 + 3 + 2 = 9$
$\therefore$ Total of cost of article = $15 \times 9 = \text{Rs.}135$ Ans
$\Rightarrow$ Profit = $180 - 135 = 45$
$\therefore$ Required Profit% = $\dfrac{45}{135} \times 100 = \dfrac{100}{3} = 33\dfrac{1}{3}\%$ Ans
$\Rightarrow$ Let cost of labour be = Rs.$3x$
$\therefore$ Cost of labour = $3x = 45$
$\Rightarrow x = \dfrac{45}{3} = \text{Rs.}15$
$\Rightarrow$ Sum of ratio = $ 4 + 3 + 2 = 9$
$\therefore$ Total of cost of article = $15 \times 9 = \text{Rs.}135$ Ans
$\Rightarrow$ Profit = $180 - 135 = 45$
$\therefore$ Required Profit% = $\dfrac{45}{135} \times 100 = \dfrac{100}{3} = 33\dfrac{1}{3}\%$ Ans
Q30. A owns a house worth Rs.50,000, He sells it to B at a profit of $15\%$. After some time B sells it back to A at $15\%$ loss. Find A's loss or gain percent.
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$\Rightarrow$ Given, A's C.P. = Rs.50,000
$\Rightarrow$ Profit = $\dfrac{15}{100} \times 50,000 = 15 \times 500 = \text{Rs.}7500$
$\therefore$ A's S.P. = $50,000 + 7500 = \text{Rs.}57,500$
$\Rightarrow$ Given, B's C.P. = Rs.57,500
$\Rightarrow$ Loss = $\dfrac{15}{100} \times 57,500 = 15 \times 575 = \text{Rs.}8625$
$\therefore$ B's S.P. = $57,500 - 8625 = \text{Rs.}48,875$
$\Rightarrow$ Now, A's C.P. = Rs.48,875
$\Rightarrow$ And, A's S.P. = Rs.57,500
$\Rightarrow$ Also, A's original Price = Rs.50,000
$\Rightarrow$ Profit = 57,500 - 48,875 = Rs.8625
$\therefore$ Profit% = $\dfrac{8625}{50,000} \times 100 = \dfrac{8625}{500} = \dfrac{1725}{100} = 17.25\%$ Ans
$\Rightarrow$ Profit = $\dfrac{15}{100} \times 50,000 = 15 \times 500 = \text{Rs.}7500$
$\therefore$ A's S.P. = $50,000 + 7500 = \text{Rs.}57,500$
$\Rightarrow$ Given, B's C.P. = Rs.57,500
$\Rightarrow$ Loss = $\dfrac{15}{100} \times 57,500 = 15 \times 575 = \text{Rs.}8625$
$\therefore$ B's S.P. = $57,500 - 8625 = \text{Rs.}48,875$
$\Rightarrow$ Now, A's C.P. = Rs.48,875
$\Rightarrow$ And, A's S.P. = Rs.57,500
$\Rightarrow$ Also, A's original Price = Rs.50,000
$\Rightarrow$ Profit = 57,500 - 48,875 = Rs.8625
$\therefore$ Profit% = $\dfrac{8625}{50,000} \times 100 = \dfrac{8625}{500} = \dfrac{1725}{100} = 17.25\%$ Ans