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## Arithmetic: Profit and Loss Test-3

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Question 1 |

By selling 18 chocolates, a vendor loses the selling price of 2 chocolates. Find his loss percent.

9% | |

10% | |

11% | |

12% |

Question 1 Explanation:

If the S.P. of 1 chocolate be Re. 1, then,

S.P. of 18 chocolates = Rs.18

C.P. = 18 + 2 = Rs.20

$ \displaystyle \therefore \,\,\,Loss\,\,\,percent=\frac{2}{20}\times 100=10%$

S.P. of 18 chocolates = Rs.18

C.P. = 18 + 2 = Rs.20

$ \displaystyle \therefore \,\,\,Loss\,\,\,percent=\frac{2}{20}\times 100=10%$

Question 2 |

A vendor sells calculators at the rate of Rs.250 each and earns a commission of 20% on each. He also sells pens at the rate of Rs.50 each and earns a commission of 10% on each. How much amount of commission will he earn in three days if he sells 10 calculators and 5 pens a day?

Rs.1, 575 | |

Rs.1, 445 | |

Rs.1, 550 | |

Rs.1, 450 |

Question 2 Explanation:

Commission on 1 calculator

$ \displaystyle \frac{250\times 20}{100}=Rs.50$

Commission on 1 pen

$ \displaystyle =\frac{50\times 10}{100}=Rs.5$

Therefore required amount of commission

$ \displaystyle \begin{array}{l}=Rs.3\,\left( 10\times 50+5\times 5 \right)\\=Rs.1575\end{array}$

$ \displaystyle \frac{250\times 20}{100}=Rs.50$

Commission on 1 pen

$ \displaystyle =\frac{50\times 10}{100}=Rs.5$

Therefore required amount of commission

$ \displaystyle \begin{array}{l}=Rs.3\,\left( 10\times 50+5\times 5 \right)\\=Rs.1575\end{array}$

Question 3 |

The income of a broker remains unchanged though the rate of commission is increased from 4 per cent to 5 per cent. The percentage of slump in business is:

10 per cent | |

15 per cent | |

20 per cent | |

30 per cent |

Question 3 Explanation:

Let the business value changes from Rs.p to Rs. y.

4% of p = 5% of y

4p/100 = 5y/100

y =4/5p

therefore change in business

x - 4/5p = p/5

Percentage slump in business

= p/5 x 1/p x 100 = 20%

4% of p = 5% of y

4p/100 = 5y/100

y =4/5p

therefore change in business

x - 4/5p = p/5

Percentage slump in business

= p/5 x 1/p x 100 = 20%

Question 4 |

If the cost price of 24 articles is equal to the selling price of 21 articles, what is the percentage gain or loss?

$ \displaystyle 14\frac{2}{7}%\,\,$ gain | |

$ \displaystyle 14\frac{2}{7}%\,\,\,$ loss | |

12.5% loss | |

12.5% gain |

Question 4 Explanation:

Percentage gain

(24 -21)/21 x 100 = 100/7%

$ \displaystyle =14\frac{2}{7}%$

(24 -21)/21 x 100 = 100/7%

$ \displaystyle =14\frac{2}{7}%$

Question 5 |

. Profit earned by an organization is distributed among officers and clerks in the ratio of 5: 3 respectively. If the number of officers is 45 and the number of clerks is 80 and the amount received by each officer is Rs.25, 000, what was the total amount of profit earned?

Rs.22 lakhs | |

Rs.18.251akhs | |

Rs.18 lakhs | |

Rs.23.25 lakhs |

Question 5 Explanation:

Profit received by each officer = Rs.25000

Therefore profit received by each clerk

3/5 x 25000 =Rs. 15000

Total earned profit

$ \displaystyle \begin{array}{l}=Rs.\,\left( 45\times 25000+80\times 15000 \right)\\=Rs.\,\left( 1125000+1200000 \right)\\=Rs.23.25\,lakh\end{array}$

Therefore profit received by each clerk

3/5 x 25000 =Rs. 15000

Total earned profit

$ \displaystyle \begin{array}{l}=Rs.\,\left( 45\times 25000+80\times 15000 \right)\\=Rs.\,\left( 1125000+1200000 \right)\\=Rs.23.25\,lakh\end{array}$

Question 6 |

A watch is sold at a profit of 20%. If both the cost price and the selling price of the watch are decreased by Rs.100, the profit would be 5%more. Original cost price of the watch is

Rs.450 | |

Rs.500 | |

Rs.550 | |

Rs.600 |

Question 6 Explanation:

Let the CP of the watch be Rs. x

$ \displaystyle \begin{array}{l}\therefore \,\,\,First\,\,\,SP=\frac{120x}{100}=Rs.\frac{6x}{5}\\Case\,II,\\CP=Rs.\left( x-100 \right)\\SP=Rs.\left( \frac{6x}{5}-100 \right)\\\Pr ofit=\left( \frac{6x}{5}-x \right)=Rs.\frac{x}{5}\\\therefore \,\,\frac{\frac{x}{5}}{x-100}\times 100=25\\\Rightarrow 25x-2500=20x\\\Rightarrow 5x=2500\\\Rightarrow x=\frac{2500}{5}=Rs.500\end{array}$

$ \displaystyle \begin{array}{l}\therefore \,\,\,First\,\,\,SP=\frac{120x}{100}=Rs.\frac{6x}{5}\\Case\,II,\\CP=Rs.\left( x-100 \right)\\SP=Rs.\left( \frac{6x}{5}-100 \right)\\\Pr ofit=\left( \frac{6x}{5}-x \right)=Rs.\frac{x}{5}\\\therefore \,\,\frac{\frac{x}{5}}{x-100}\times 100=25\\\Rightarrow 25x-2500=20x\\\Rightarrow 5x=2500\\\Rightarrow x=\frac{2500}{5}=Rs.500\end{array}$

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