31. There is a profit of 20% on the cost price of an article. The % of profit, when calculated on selling price is
(a) \(\displaystyle 16\frac{2}{3}\%\)
(b) 20%
(c) \(\displaystyle 33\frac{1}{3}\%\)
(d) 25%
(e) None of these
Solution: (a)
C.P. of article =₹ x
Gain = \(\displaystyle \frac{{6X}}{5}-x=\frac{{6x-5x}}{5}\)
= \(\displaystyle \frac{x}{5}\)
Gain percent = \(\displaystyle \frac{{gain}}{{sp}}\times 100\)
= \(\displaystyle \frac{{\frac{x}{5}}}{{\frac{{6x}}{5}}}\times 100\)
= \(\displaystyle \frac{{50}}{3}=16\frac{2}{3}\%\)
32. Pooja wants to sell a watch at a profit of 20%. She bought it at 10% less and sold it at ₹30 less, but still she gained 20%. The cost price of watch is
(a) ₹240
(b) ₹220
(c) ₹250
(d) ₹225
(e) ₹275
Solution: (c)
C.P. of watch = Rs. x (let)
S.P. = \(\displaystyle \frac{{120x}}{{100}}=Rs.\frac{{6x}}{5}\)
Case II,
C.P. = \(\displaystyle Rs.\frac{{9x}}{{10}}\)
S.P. = Rs. \(\displaystyle (\frac{{6X}}{5}-30)\)
According to the question,
\(\displaystyle \frac{{6X}}{5}-30=\frac{{9X}}{{10}}\times \frac{{120}}{{100}}=\frac{{27X}}{{25}}\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{6X}}{5}-\frac{{27X}}{{25}}=30\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{30X-27X}}{{25}}=30\)
\(\displaystyle \Rightarrow \)\(\displaystyle 3x=30\times 25\)
\(\displaystyle \Rightarrow \)\(\displaystyle X=\frac{{30\times 25}}{3}=RS.250\)
33. There is 10% loss if an article is sold at Rs. 270. Then the cost price of the article is
(a) Rs. 300
(b) Rs. 270
(c) Rs. 320
(d) Rs. 250
(e) Rs. 280
Solution: (a)
C.P. of article = Rs. x (let).
According to the question
\(\displaystyle \frac{{x\times 90}}{{100}}=270\)
x = \(\displaystyle \frac{{270\times 100}}{{90}}=Rs.300\)
34. By selling an article for Rs. 450, I lose 20%. For what price should I sell it to gain 20% ?
(a) Rs. 490
(b) Rs. 675
(c) Rs. 470
(d) Rs. 562.50
(e) Rs. 580
Solution: (b)
C.P of article = \(\displaystyle \frac{{100}}{{100-20}}\times 450\)
= \(\displaystyle \frac{{100\times 450}}{{80}}=Rs.562.5\)
Therefore, to gain 20%
S.P. = \(\displaystyle \frac{{562.5\times 120}}{{100}}=Rs.675\)
35. The C.P of 10 articles is equal to the S.P. of 15 articles. What is the profit or loss percentage?
(a) 25.5%
(b) 35%
(c) 10%
(d) 33.3%
(e) 36.2%
Solution: (d)
Let C.P. of each article be Re.1.
C.P. of 15 articles = Rs. 15
Their S.P. = Rs. 10
Therefore, Loss percent = \(\displaystyle \frac{{15-10}}{{15}}\times 100\)
= \(\displaystyle \frac{{100}}{3}=33.3\%\)
36. By selling a bag at Rs. 230, profit of 15% is made. The selling price of the bag, when it is sold at 20% profit would be
(a) Rs. 250
(b) Rs. 205
(c) Rs. 240
(d) Rs. 200
(e) Rs. 280
Solution: (c)
Let the C.P. of bag be Rs. x.
According to the question,
\(\displaystyle x\times \frac{{115}}{{100}}=230\)
x = \(\displaystyle \frac{{230\times 100}}{{115}}=200\)
For profit of 20%,
S.P. of bag = Rs. \(\displaystyle \frac{{200\times 120}}{{100}}=240\)
37. A man gains 20% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be
(a) 40%
(b) 100%
(c) 120%
(d) 140%
(e) 150%
Solution: (d)
Let the cost price of article be Rs. 100.
\(\displaystyle \Rightarrow \)First S.P. = Rs. 120
When the selling price be Rs.240,
Profit = Rs. (240 – 100) = Rs. 140
\(\displaystyle \Rightarrow \) Profit percent = \(\displaystyle \frac{{140}}{{100}}\times 100=140\%\)
38. The cost price of 25 books is equal to the selling price of 20 books. The profit percent is
(a) 20%
(b) 22%
(c) 24%
(d) 25%
(e) 28%
Solution: (d)
Let the cost price of each book be Re. 1.
Therefore, C.P. of 20 books = Rs. 20
S.P. of 20 books = Rs. 25
Profit percent = \(\displaystyle \frac{{25-20}}{{20}}\times 100\)
= \(\displaystyle \frac{{5\times 100}}{{20}}=25\%\)
39. By selling a tape-recorder for Rs. 1040 a man gains 4%. If he sells it for Rs. 950, his loss will be
(a) 5%
(b) 4%
(c) 4.5%
(d) 9%
(e) 8%
Solution: (a)
C.P. of taperecorder = Rs. \(\displaystyle \frac{{100}}{{104}}\times 1040\)
= Rs. 1000
On selling for Rs. 950,
Loss = Rs. (1000 – 950)
= Rs. 50
Therefore, Loss percent = \(\displaystyle \frac{{50\times 100}}{{1000}}=5\%\)
40. By what fraction selling price (S.P.) must be multiplied to get the cost price (C.P.) if the loss is 20%?
(a) \(\displaystyle \frac{4}{5}\)
(b) \(\displaystyle \frac{8}{5}\)
(c) \(\displaystyle \frac{5}{4}\)
(d) \(\displaystyle \frac{6}{5}\)
(e) \(\displaystyle \frac{3}{5}\)
Solution: (c)
According to the question,
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{80}}{{100}}ofC.P.=S.P.\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{4}{5}ofC.P.=S.P.\)
\(\displaystyle \Rightarrow \)\(\displaystyle C.P.=S.P.\times \frac{5}{4}\)
