41. To make a profit of 20% the selling price of the goods is Rs. 240. The cost price of the goods is:
(a) Rs. 200
(b) Rs. 210
(c) Rs. 220
(d) Rs. 230
(e) Rs. 250
Solution: (a)
According to the question,
C.P. of article = \(\displaystyle (\frac{{100}}{{100+profit\%}})\times S.P.\)
= Rs. \(\displaystyle (\frac{{100}}{{120}}\times 240)\)
= Rs. 200
42. The per cent profit made when an article is sold for Rs. 78 is twice as much as when it is sold for Rs. 69. The cost price of the article is
(a) Rs. 60
(b) Rs. 51
(c) Rs. 55.50
(d) Rs. 70
(e) Rs. 50
Solution: (a)
Let the C.P. of article be Rs. x.
According to the question,
78 – x = 2 (69– x)
78 – x = 138 – 2x
2x – x = 138 – 78
x = Rs. 60
42. A man sold an item for ₹7,500 and incurred a loss of 25%. At what price should he have sold the item to have gained a profit of 25%?
(a) ₹13,800
(b) ₹12,500
(c) ₹11,200
(d) Cannot be determined
(e) None of these
Solution: (b)
Let Cost Price of article be x
S.P = \(\displaystyle x-\frac{{25}}{{100}}x=7500\)
\(\displaystyle \frac{{75}}{{100}}x=7500\)
x= \(\displaystyle \frac{{7500\times 100}}{{75}}=10000\)
S.P. of article to have gain 25% = \(\displaystyle 1000+\frac{{20}}{{100}}\times 10000\)
= ₹ 12500
43. Sarita earned a profit of 30 per cent on selling an article for ₹6,110. What was the cost price of the article?
(a) ₹5,725
(b) ₹4,080
(c) ₹5,250
(d) ₹4,400
(e) None of these
Solution: (e)
Let Cost Price of article be x
Selling Price, S.P = \(\displaystyle x+\frac{{30}}{{100}}x=6110\)
\(\displaystyle \frac{{130}}{{100}}x=6110x=\frac{{6110\times 100}}{{130}}=4700\)
Cost Price of article is ₹ 4,700.
44. Sujit incurred a loss of 45 percent on selling an article for ₹3,740. What was the cost price of the article?
(a) ₹5,725
(b) ₹5,080
(c) ₹6,250
(d) ₹6,400
(e) None of these
Solution: (e)
Let Cost Price of article be x
According to question
\(\displaystyle x-\frac{{45}}{{100}}x=3740\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{55}}{{100}}=3740\)
\(\displaystyle \Rightarrow \) x=6800
45. Mehul sold an item for ₹5,625 and incurred a loss of 25%. At what price should he have sold the item to gain a profit of 25%?
(a) ₹9,375
(b) ₹10,500
(c) ₹8,250
(d) Cannot be determined
(e) None of these
Solution: (a)
Let Cost Price of item be x
Selling Price = \(\displaystyle x-\frac{{25}}{{100}}x=5625\)
\(\displaystyle \frac{{75x}}{{100}}=5625\)
\(\displaystyle x=5625\times \frac{{100}}{{75}}=7500\)
Selling Price after gaining 25%
S.P. = \(\displaystyle 7500+\frac{{25}}{{100}}\times 7500=9375\)
46. Kartik sold an item for ₹ 6,500 and incurred a loss of 20%. At what price should he have sold the item to have gained a profit of 20%?
(a) ₹10,375
(b) ₹ 9,750
(c) ₹ 8,125
(d) Cannot be determined
(e) None of these
Solution: (b)
Let Cost Price item be x
Its Selling Price = \(\displaystyle x-\frac{{20}}{{100}}x=6500\)
\(\displaystyle \frac{{80x}}{{100}}=6500\)
x= \(\displaystyle 6500\times \frac{{100}}{{80}}=8125\)
S.P of item to have gained a Profit of 20%
= \(\displaystyle 8125+\frac{{20}}{{100}}\times 8125=9750\)
47. Manoj incurred a loss of 40 percent on selling an article for ₹ 5,700. What was the cost price of the article?
(a) ₹ 7,725
(b) ₹ 9,080
(c) ₹ 8,250
(d) ₹9,400
(e) None of these
Solution: (e)
Let Cost Price of article be x
\(\displaystyle x-\frac{{40}}{{100}}x=5700\)
\(\displaystyle \frac{{60}}{{100}}x=5700\)
x = \(\displaystyle \frac{{5700\times 100}}{{60}}=9750\)
Cost Price of the article is ₹ 9,500
48. Raj sold an item for ₹ 6,384 and incurred a loss of 30%. At what price should he have sold the item to have gained a profit of 30%?
(a) ₹14,656
(b) ₹11,856
(c) ₹13,544
(d) Cannot be determined
(e) None of these
Solution: (b)
Let cost price of item be x
\(\displaystyle x-\frac{{30}}{{100}}x=6384\)
\(\displaystyle \frac{{70x}}{{100}}=6384\)
\(\displaystyle x=6384\times \frac{{100}}{{70}}=9120\)
SP of item with 30% Profit = 1.3x = 1.3 × 9120= ₹ 11,856
49. A dishonest dealer prefers to sell his goods at cost price but uses less weight for a kg weight and gains \(\displaystyle 4\frac{1}{6}\%\) What does he use for a kg weight?
(a) 950 gm
(b) 980 gm
(c) 960 gm
(d) 840 gm
(e) None of these
Solution: (c)
\(\displaystyle 100\times \frac{{1000}}{x}-100=\frac{{25}}{6}\)
\(\displaystyle \Rightarrow \)x = 960 gm
Alternate method:
Let the error is x gms and profit is= \(\displaystyle 4\frac{1}{6}\%=\frac{{25}}{6}\%\)
So we have ,
\(\displaystyle \begin{array}{l}\frac{{Error}}{{TrueWeight-Error}}\times 100=\%of\Pr ofit\\\frac{x}{{1000-x}}\times 100=\frac{{25}}{6}\\6\times 100x=25(1000-x)\\600x=25000-25x\\625x=25000\\x=40\end{array}\)
Therefore, error is 40gm. Hence for a kg he uses a weight of 1000−40=960gms
50. 21 articles were bought for ₹ 6531 and sold for ₹ 9954. How much was the approximate profit percentage per article ?
(a) 56%
(b) 43%
(c) 52%
(d) 49%
(e) 61%
Solution: (c)
Cost price per article = 311
Selling price per article= \(\displaystyle \frac{{9954}}{{21}}=474\)
\(\displaystyle \frac{{474-311}}{{311}}\times 100=52\%\)
