Q1. A student buys a pen for Rs 90 and sells it for Rs. 100. Find his gain and gain percent.
Sol. Given cost price of pen = Rs. 90
Selling price of pen = Rs. 100
We know that Gain = S.P – C.P
Therefore, Gain =100 – 90 = 10
$$ \text {We know that Gain% } = [\frac {\text {Gain}}{\text{CP }} \times 100 ] \% $$ $$ \therefore \text {Gain% }=\frac {10}{90} \times 100 $$ $$ = 11 \frac {1}{9} $$Q2. Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss percent.
Sol. Given Rekha bought a saree for Rs. 1240
Rekha Sold the saree for Rs. 1147
We know that Loss = CP – SP
Therefore, Loss = 1240 – 1147 = 93
$$ \text {We know that Loss% } = [\frac {\text {Loss}}{\text{CP }} \times 100 ] \% $$ $$ \therefore \text {Loss% }=\frac {93}{1240} \times 100 = 7.5 \% $$Q3. A boy buys 9 apples for Rs 9.60 and sells them at 11 for Rs 12. Find his gain or loss percent.
Sol. Given that the cost price of 9 apples is Rs 9.60
$$ \therefore \text {The cost price of 1 apple (Rs.)} = \frac {9.60}{9} $$ $$ \text {Given that Selling price of 11 apple (Rs.) } =12 $$ $$ \therefore \text {The selling price of 1 apple (Rs.) } = \frac {12}{11} $$$$ \text {Now, } SP – CP = \frac {12}{11} – \frac {9.60}{9} = \frac {2.40}{99} $$ $$ = Gain \quad \quad [\because \text {SP- CP > 0} ] $$$$ \text {We know that Gain% } = [\frac {\text {Gain}}{\text{CP }} \times 100 ] \% $$ $$ \therefore \text {Gain% }=\frac {\frac {2.40}{99} }{\frac {9.60}{9} } \times 100 $$ $$ = \frac {25}{11} = 2 \frac {3}{11} \% $$Q4. The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.
Sol.
Let assume the CP of 1 article be Rs x.
And assume that SP of 1 article be Rs y.
Given that the cost price of 10 article is equal to selling price of 9 article.
$$ \Rightarrow \quad 10x = 9y $$ $$ \Rightarrow \quad y = \frac {10}{9}x $$$$ \Rightarrow \text {Cost price is less than selling price. So there is profit.} $$ Profit = SP – CP
$$ =\frac{10}{9}x – x = \frac {x}{9} $$$$ \text {As we know that Profit %} = \frac {\text {Profit}}{\text {CP}} \times 100 $$ $$ = \frac {\frac {x}{9}}{x} \times 100 $$ $$ =\frac {100}{9} \% $$Q5. A retailer buys a radio for Rs. 225. His overhead expenses are Rs. 15. If he sells the radio for Rs. 300, determine his profit percent.\begin{array}{l} \text {Sol. } \\ \text {Total cost of Radio } = \text {CP of radio } + \text { Overhead expenses } =225+15= \text {Rs. }240 \\ \text {SP of radio is Rs. 300} \\\text {Profit = SP – CP }=300-240= \text { Rs. }60 \\ \text {As we know that Profit %} = \frac {\text {Profit}}{\text {CP}} \times 100 \\ \Rightarrow \text {Profit %} = \frac {\text {60}}{240} \times 100 \\ =25 \% \end{array}Q6. A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he sells the cooler for Rs 1550, determine his profit percent.\begin{array}{l} \text {Sol. } \\ \text {Total cost of cooler } = \text {CP of radio } + \text { Overhead expenses } =1200+40= \text {Rs. }1240 \\ \text {SP of radio is Rs. 1550} \\\text {Profit = SP – CP }=1550-1240= \text { Rs. }310 \\ \text {As we know that Profit %} = \frac {\text {Profit}}{\text {CP}} \times 100 \\ \Rightarrow \text {Profit %} = \frac {\text {310}}{1240} \times 100 \\ =25 \% \end{array}Q7. A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells the same for Rs. 300, find his profit percent.\begin{array}{l} \text {Sol. } \\ \text {Total cost of wristwatch } = \text {CP of wristwatch } + \text { repair expenses } =225+15= \text {Rs. }240 \\ \text {SP of radio is Rs. 300} \\\text {Profit = SP – CP }=300-240= \text { Rs. }60 \\ \text {As we know that Profit %} = \frac {\text {Profit}}{\text {CP}} \times 100 \\ \Rightarrow \text {Profit %} = \frac {\text {60}}{240} \times 100 \\ =25 \% \end{array}Q8. Ramesh bought two boxes for Rs. 1300. He sold one box at a profit of 20 % and the other box at a loss of 12 %. If the selling price of both boxes is the same, find the cost price of each box.\begin{array}{l} \text {Sol. } \\\text {Given that cost price of two boxes } = \text {Rs. } 1300 \\ \text {Let’s assume cost price of one box be Rs x.} \\ \Rightarrow \text {Cost price of other box }= \text {Rs. }1300-x \\\text {Profit on first box is 20 % } \\ \Rightarrow \text {SP of first box } = x + 20\% \text { of } \times x \\ \Rightarrow \quad \text {SP of first box } = x + \frac {20}{100} x \\ \Rightarrow \quad \text {SP of first box } = \frac {6}{5} x \\\text {Loss on second box is 12 % } \\ \Rightarrow \text {SP of second box } = (1300 -x ) – 12\% \text { of } \times (1300 -x ) \\ \Rightarrow \text {SP of second box } = (1300 -x ) – \frac {12}{100} \times (1300 -x ) \\ \Rightarrow \quad \text {SP of second box } = \frac {28600-22x}{25} \\ \text {Its given that SP of both boxes are same, so we get} \\\frac {6}{5} x = \frac {28600-22x}{25} \\ \Rightarrow \quad 150 x=28600 \times 5 – 110 x \\ \Rightarrow \quad 150 x+110 x=28600 \times 5 \\ \Rightarrow \quad 260 x=28600 \times 5 \\ \Rightarrow \quad x=\frac {28600 \times 5}{260} \\ \Rightarrow \quad =550 \\ \therefore \text {Cost price of first box }=\text {Rs. } 550 \\ \text {And cost price of second box }=1300- 550=\text {Rs. } 750 \\ \end{array}
Sol. Given cost price of pen = Rs. 90
Selling price of pen = Rs. 100
We know that Gain = S.P – C.P
Therefore, Gain =100 – 90 = 10
$$ \text {We know that Gain% } = [\frac {\text {Gain}}{\text{CP }} \times 100 ] \% $$ $$ \therefore \text {Gain% }=\frac {10}{90} \times 100 $$ $$ = 11 \frac {1}{9} $$Q2. Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss percent.
Sol. Given Rekha bought a saree for Rs. 1240
Rekha Sold the saree for Rs. 1147
We know that Loss = CP – SP
Therefore, Loss = 1240 – 1147 = 93
$$ \text {We know that Loss% } = [\frac {\text {Loss}}{\text{CP }} \times 100 ] \% $$ $$ \therefore \text {Loss% }=\frac {93}{1240} \times 100 = 7.5 \% $$Q3. A boy buys 9 apples for Rs 9.60 and sells them at 11 for Rs 12. Find his gain or loss percent.
Sol. Given that the cost price of 9 apples is Rs 9.60
$$ \therefore \text {The cost price of 1 apple (Rs.)} = \frac {9.60}{9} $$ $$ \text {Given that Selling price of 11 apple (Rs.) } =12 $$ $$ \therefore \text {The selling price of 1 apple (Rs.) } = \frac {12}{11} $$$$ \text {Now, } SP – CP = \frac {12}{11} – \frac {9.60}{9} = \frac {2.40}{99} $$ $$ = Gain \quad \quad [\because \text {SP- CP > 0} ] $$$$ \text {We know that Gain% } = [\frac {\text {Gain}}{\text{CP }} \times 100 ] \% $$ $$ \therefore \text {Gain% }=\frac {\frac {2.40}{99} }{\frac {9.60}{9} } \times 100 $$ $$ = \frac {25}{11} = 2 \frac {3}{11} \% $$Q4. The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.
Sol.
Let assume the CP of 1 article be Rs x.
And assume that SP of 1 article be Rs y.
Given that the cost price of 10 article is equal to selling price of 9 article.
$$ \Rightarrow \quad 10x = 9y $$ $$ \Rightarrow \quad y = \frac {10}{9}x $$$$ \Rightarrow \text {Cost price is less than selling price. So there is profit.} $$ Profit = SP – CP
$$ =\frac{10}{9}x – x = \frac {x}{9} $$$$ \text {As we know that Profit %} = \frac {\text {Profit}}{\text {CP}} \times 100 $$ $$ = \frac {\frac {x}{9}}{x} \times 100 $$ $$ =\frac {100}{9} \% $$Q5. A retailer buys a radio for Rs. 225. His overhead expenses are Rs. 15. If he sells the radio for Rs. 300, determine his profit percent.\begin{array}{l} \text {Sol. } \\ \text {Total cost of Radio } = \text {CP of radio } + \text { Overhead expenses } =225+15= \text {Rs. }240 \\ \text {SP of radio is Rs. 300} \\\text {Profit = SP – CP }=300-240= \text { Rs. }60 \\ \text {As we know that Profit %} = \frac {\text {Profit}}{\text {CP}} \times 100 \\ \Rightarrow \text {Profit %} = \frac {\text {60}}{240} \times 100 \\ =25 \% \end{array}Q6. A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he sells the cooler for Rs 1550, determine his profit percent.\begin{array}{l} \text {Sol. } \\ \text {Total cost of cooler } = \text {CP of radio } + \text { Overhead expenses } =1200+40= \text {Rs. }1240 \\ \text {SP of radio is Rs. 1550} \\\text {Profit = SP – CP }=1550-1240= \text { Rs. }310 \\ \text {As we know that Profit %} = \frac {\text {Profit}}{\text {CP}} \times 100 \\ \Rightarrow \text {Profit %} = \frac {\text {310}}{1240} \times 100 \\ =25 \% \end{array}Q7. A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells the same for Rs. 300, find his profit percent.\begin{array}{l} \text {Sol. } \\ \text {Total cost of wristwatch } = \text {CP of wristwatch } + \text { repair expenses } =225+15= \text {Rs. }240 \\ \text {SP of radio is Rs. 300} \\\text {Profit = SP – CP }=300-240= \text { Rs. }60 \\ \text {As we know that Profit %} = \frac {\text {Profit}}{\text {CP}} \times 100 \\ \Rightarrow \text {Profit %} = \frac {\text {60}}{240} \times 100 \\ =25 \% \end{array}Q8. Ramesh bought two boxes for Rs. 1300. He sold one box at a profit of 20 % and the other box at a loss of 12 %. If the selling price of both boxes is the same, find the cost price of each box.\begin{array}{l} \text {Sol. } \\\text {Given that cost price of two boxes } = \text {Rs. } 1300 \\ \text {Let’s assume cost price of one box be Rs x.} \\ \Rightarrow \text {Cost price of other box }= \text {Rs. }1300-x \\\text {Profit on first box is 20 % } \\ \Rightarrow \text {SP of first box } = x + 20\% \text { of } \times x \\ \Rightarrow \quad \text {SP of first box } = x + \frac {20}{100} x \\ \Rightarrow \quad \text {SP of first box } = \frac {6}{5} x \\\text {Loss on second box is 12 % } \\ \Rightarrow \text {SP of second box } = (1300 -x ) – 12\% \text { of } \times (1300 -x ) \\ \Rightarrow \text {SP of second box } = (1300 -x ) – \frac {12}{100} \times (1300 -x ) \\ \Rightarrow \quad \text {SP of second box } = \frac {28600-22x}{25} \\ \text {Its given that SP of both boxes are same, so we get} \\\frac {6}{5} x = \frac {28600-22x}{25} \\ \Rightarrow \quad 150 x=28600 \times 5 – 110 x \\ \Rightarrow \quad 150 x+110 x=28600 \times 5 \\ \Rightarrow \quad 260 x=28600 \times 5 \\ \Rightarrow \quad x=\frac {28600 \times 5}{260} \\ \Rightarrow \quad =550 \\ \therefore \text {Cost price of first box }=\text {Rs. } 550 \\ \text {And cost price of second box }=1300- 550=\text {Rs. } 750 \\ \end{array}