21. An article is marked at ₹18,000. A trader bought it at successive discounts of 25% and 10% respectively. He spent ₹1,350 on its transportation to his shop and then sold the article for ₹15,000. What is trader’s profit% in the whole transaction?
(a) \(\displaystyle 16\frac{2}{3}\%\)
(b) 28%
(c) 30%
(d) \(\displaystyle 11\frac{1}{9}\%\)
(e) 20%
Solution: (d)
He bought the article for
\(\displaystyle \left[ {\left( {\frac{{100-25}}{{100}}} \right)} \right]\left[ {\left( {\frac{{100-10}}{{100}}} \right)} \right]\times 18000=12150\)
Spent 1350 on repairs,
Total CP = 1350 + 12150 = 13,500
SP = 15,000
So profit% = \(\displaystyle \frac{{1500}}{{13500}}\times 100=11\frac{1}{9}\%\)
22. Shopkeeper purchased some goods for ₹900 and sold one third of the goods at a loss of what 12%, then at gain % should the remainder goods he sold to gain 18% profit on the whole transaction?
23. A milkman bought 70 litres of milk for 630 and added 5 litres of water. If he sells it at 9.00 per litre, his profit percentage isof 7%. The cost price of that article is
(a) \(\displaystyle 8\frac{1}{5}\%\)
(b) 7%
(c) \(\displaystyle 8\frac{1}{5}\%\)
(d) \(\displaystyle 7\frac{1}{7}\%\)
(e) \(\displaystyle 6\frac{2}{9}\%\)
Solution: (d)
CP of 75 litres of mixture of milk and water =₹ 630
SP of 75 litres of mixture of milk and water = 9 × 75 = ₹675
Gain = 675 – 630 =₹ 45
Gain percent = \(\displaystyle \frac{{45}}{{630}}\times 100\)
= \(\displaystyle \frac{{50}}{7}=7\frac{1}{7}\%\)
24. In terms of percentage profit, which is the best transaction? C.P. (in ₹ ) Profit (In ₹ )
(I) CP=36 Profit=17
(II) CP=50 Profit=24
(III) CP=40 Profit=19
(IV) CP=60 Profit=29
(V) CP=70 Profit=20
(a) I
(b) II
(c) III
(d) IV
(e) V
Solution: (d)
Case I : Percentage Profit
\(\displaystyle \frac{{17\times 100}}{{36}}=47\%\)
Case II : Percentage Profit
\(\displaystyle \frac{{24\times 100}}{{50}}=48\%\)
Case III : Percentage Profit
\(\displaystyle \frac{{19\times 100}}{{40}}=47.5\%\)
Case IV : Percentage Profit
\(\displaystyle \frac{{29\times 100}}{{60}}=48.3\%\)
Case V : Percentage Profit
\(\displaystyle \frac{{20\times 100}}{{70}}=28.6\%\)
Alternate method
In such type of pattern based question adopt option approach,
1st – Check largest value of cost price
2nd – Check smallest value of cost price
mark the answer which is greatest
\(\displaystyle \begin{array}{l}1st=\frac{{29}}{{60}}\times 100=48.33\\2nd=\frac{{17}}{{36}}\times 100=47.22(wrong)\end{array}\)
25. If the cost price is 95% of the selling price, what is the profit percent ?
(a) 4%
(b) 4.75%
(c) 5%
(d) 5.26%
(e) 6%
Solution: (d)
If the cost price be ₹ x, then
S.P. = \(\displaystyle \frac{{100}}{{95}}X=\frac{{20}}{{19}}X\)
Gain = \(\displaystyle \frac{{20X}}{{19}}-X=\frac{X}{{19}}\)
Gain percent = \(\displaystyle \frac{{\frac{X}{{19}}}}{X}\times 100=5.26\%\)
Aliter :
Here C.P. = \(\displaystyle \frac{{95}}{{100}}SP\)
C.P. = \(\displaystyle SP(\frac{{100}}{{100+profit\%}})\)
9500 + 95 profit% = 10000
Profit % = \(\displaystyle \frac{{500}}{{95}}\)
Profit % = 5.26%
26. Krishnan bought a camera and paid 20% less than its original price. He sold it at 40% profit on the price he had paid. The percentage of profit earned by Krishnan on the original price was
(a) 22%
(b) 32%
(c) 12%
(d) 15%
(e) 25%
Solution: (c)
Let the original price be ₹ x.
= \(\displaystyle \frac{{80}}{{100}}\times x=\frac{{4x}}{5}\)
SP = \(\displaystyle \frac{{4x}}{5}\times \frac{{140}}{{100}}=\frac{{28x}}{{25}}\)
Gain on original price
= \(\displaystyle \frac{{28x}}{{25}}-x=\frac{{3x}}{{25}}\)
Gain % = \(\displaystyle \frac{{3x}}{{25x}}\times 100=12\%\)
27. By what percent must the cost price be raised in fixing the sale price in order that there may be a profit of 20% after allowing a commission of 10% ?
So the 33.33% must be added to the cost so that profit of 20% is made after giving 10% discount
Shortcut %raise= \(\displaystyle \frac{{30}}{{90}}\times 100\) =33.33% or \(\displaystyle 33\frac{1}{3}\%\)
28. A man purchased a bed sheet for ₹ 450 and sold it at a gain of 10% calculated on the selling price. The selling price of the bed sheet was
(a) ₹ 460
(b) ₹ 475
(c) ₹ 480
(d) ₹ 500
(e) ₹550
Solution: (d)
Let the S.P. of the bedsheet be Rs. x.
\(\displaystyle \Rightarrow \)\(\displaystyle 450+\frac{{10\times X}}{{100}}=X\)
\(\displaystyle \Rightarrow \)\(\displaystyle X-\frac{X}{{10}}=450\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{9X}}{{10}}=450\)
\(\displaystyle \Rightarrow \) x = \(\displaystyle \frac{{450\times 10}}{9}=500\)
Alternate method :
C.P. = Rs. 450,
Profit = \(\displaystyle \frac{{10SP}}{{100}}=\frac{{SP}}{{10}}\)
Profit = S.P. – C.P.
\(\displaystyle \frac{{SP}}{{10}}=SP-450\)
\(\displaystyle 450=SP-\frac{{SP}}{{10}}\)
S.P. = \(\displaystyle \frac{{450\times 10}}{9}=500\)
29. A retailer buys a radio for ₹225. His overhead expenses are ₹15. He sells the radio for ₹300. The profit per cent of the retailer is :
(a) 25%
(b) \(\displaystyle 26\frac{2}{3}\%\)
(c) 20%
(d) \(\displaystyle 33\frac{1}{3}\%\)
(e) 30%
Solution: (a)
Actual C.P. = 225 + 15 = ₹240
Gain = 300 – 240 = ₹60
Gain percent = \(\displaystyle \frac{{60}}{{240}}\times 100=25\%\)
30. If books bought at prices from ₹150 to ₹300 are sold at prices ranging from ₹250 to ₹350, what is the greatest possible profit that might be made in selling 15 books?
(a) Cannot be determined
(b) ₹750
(c) ₹ 4,250
(d) ₹3,000
(e) ₹3,500
Solution: (d)
Minimum cost price = 150 × 15 = ₹2250
Maximum selling price = 350 × 15 = ₹5250
Gain = 5250 – 2250 = ₹3000
[150 being the lowest & 350 being the highest price]
