Profit and Loss Questions - 1

A trader sold an article at a profit of 20% for Rs.360. What is the cost price of the article ?
  • Rs.270
  • Rs.300
  • Rs.280
  • Rs.320
  • Rs.315
Explanation   

Cost Price = $\displaystyle \dfrac{\text{Selling Price}}{100 + \text{Profit}\%} \times 100 => \ \dfrac{360}{100 + 20} \times 100 => \frac{360}{120} \times 100$ = Rs.300

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A trader sold an article at a loss of 20% for Rs.360. What is the cost price of the article ?
  • Rs.400
  • Rs.500
  • Rs.450
  • Rs.540
  • Rs.390
Explanation   

Cost Price = $\displaystyle \frac{\text{Selling Price}}{100 - \text{Profit}\%} \times 100 => \frac{360}{100 - 20} \times 100 => \frac{360}{80} \times 100$ = Rs.450

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A trader sold an article for Rs.540 and incurred a loss of 10%. At what price should he sell the article to gain 20% ?
  • Rs.660
  • Rs.840
  • Rs.800
  • Rs.720
  • Rs.750
Explanation   

Selling price to gain 20% = $\displaystyle \frac{540}{100 - 10} \times 120 = \frac{540}{90} \times 120 $ = 720.

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By selling an article, a trader gained 24%. If he had sold it for Rs.72 more, he would have gained a profit of 30%. What is the cost price of the article ?
  • Rs.900
  • Rs.840
  • Rs.125
  • Rs.950
  • Rs.1200
Explanation   

Let cost price be 100 or 100%

Then selling price = 100 + 24% = 124 or 124%

If sold at Rs.72 more => 130% = then 124% + Rs.72 = 130%

130% - 124% = Rs.72 = > 6% = 72 => cost price = $\displaystyle \frac{72}{6} \times 100 $ = Rs.1200

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The cost price of 12 pens is equal to the selling price of 10 pens. What is the profit percentage ?
  • 15%
  • 20%
  • 12%
  • 10%
  • 8%
Explanation   

Let cost price of 1 pen be Rs.1, then cost price of 12 pens = Rs.12.

Cost price of 10 pens = Rs.10

S.P of 10 pens = C.P of 12 => profit = 12 – 10 = Rs.2

Profit % = $\displaystyle \frac{2}{10} \times $ 100 = 20%

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A trader marks the price of an article 25% above the cost price and allows a discount of 10%. What is the profit percentage ?
  • 20%
  • 10%
  • 15%
  • 12.5%
  • 25%
Explanation   

Let C.P be 100, then Marked Price = 100 + 100 x 25% = 125

Discount @ 10% on M.P = 125 – 12.5 = 112.5

Profit = 112.5 – 100 = 12.5

Profit % = $\displaystyle \frac{12.5}{100} \times 100$ = 12.5%

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Price of 6 note books and 4 pens is Rs.140, or the price of 4 note books and 6 pens is Rs.160. What is the price of 1 Note Book and 1 Pen respectively ?
  • Rs.10, Rs.20
  • Rs. 30, Rs.15
  • Rs.20, Rs.10
  • Rs.15, Rs.30
  • Can’t be determined
Explanation   
3[4NB + 6P = 160]   ..........   I
         
2[6NB + 4P = 140]   ..........   II
         
12NB + 18P = 480        
         
12NB + 8P = 280        
         
             10P = 200        

10P = 200 => Pen = Rs.20.

=> Note Book = 4NB + 6(20) = 160.

4NB = 160 – 120 = 40 => Note Book = $\displaystyle \frac{40}{4}$ = Rs.10.

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A trader sold two watches at Rs.1200 each. He sold one at a profit of 20%, and another at loss of 20%. What is the total profit or loss in the entire transaction ?
  • No profit/No loss
  • 1% Profit
  • 2% Profit
  • 1% Loss
  • 4% loss
Explanation   

When two articles are sold at equal price and at equal Profit% and Loss% then the overall effect in the transaction would be

$\displaystyle \left(\frac{\text{Profit} \% \times \ \text{Loss} \%}{100} \right) \ = \ \left(- \text{ve} \right) \text{or} \left(\text{Loss} \right) $

Overall effect = $\displaystyle \frac{20 \times 20}{100}$ = 4% loss.

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Mahi purchase two articles at Rs.1200 each and sold one at 30% profit another at 30% loss. What is the total profit or loss in the entire transaction ?
  • No profit / No loss
  • 1% Profit
  • 1% loss
  • 9% profit
  • 9% loss
Explanation   

When two articles are purchased at equal price and sold one article at P% profit and another at L% loss then overall effect would be

$\displaystyle \left(\frac{+\text{Profit}\% - \ \text{Loss}\%}{2} \right) $

[Note: If resulting value is + ve it denotes Profit and – ve it denotes loss.]

= $\displaystyle \left(\frac{+20 - 20}{2} \right) = \frac{0}{2}$ = 0 = neither profit nor loss.

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A trader purchased 10 boxes of pens, and each box contains 12 pens. He altered the number of pens in each box and sold at the price printed on the box, when purchased. Find number of pens in the box that he needs to sell to gain 20% profit ?
  • 12 pens
  • 8 pens
  • 11 pens
  • 9 pens
  • 10 pens
Explanation   

Let cost price of each pen be Rs.1

Then printed price on each box is Rs.12.

To get 20% profit, each pen be sold at Rs.1 + 1 $\displaystyle \times \frac{20\%}{100}$ = 1 + 0.2 = Rs.1.2

Printed price on each box Rs.12.

Number of pens in the box = $\displaystyle \frac{12}{1.2}$ = 10 pens.

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Profit and Loss Formulas and Shortcuts


Cost Price: Purchase price of an article.

Selling Price: The price at which an article is sold.

Marked Price: Which is fixed above the cost price. Need not to sell at the same price.

Cost Price = Selling Price – Profit

Or

Selling Price + Loss

Cost Price = $\displaystyle \frac{\text{Selling Price}}{100 + {\text Profit}\%} \times 100$

Or

Cost Price = $\displaystyle \frac{\text{Selling Price}}{100 - {\text Profit}\%} \times 100$

Selling Price = Cost Price + Profit.

Or

Cost Price – Loss

Profit % = $\displaystyle \frac{\text{Profit}}{\text{Cost Price}} \times 100$

Loss % = $\displaystyle \frac{\text{Loss}}{\text{Cost Price}} \times 100$

When two articles are sold at equal price and at equal Profit% and Loss% then the overall effect in the transaction would be

$\displaystyle \left(\frac{\text{Profit} \% \times {\text Loss \%}}{100} \right)$ = (- ve) or (Loss)

When two articles are purchased at equal price and sold one article at P% profit and another at L% loss then overall effect would be

$\displaystyle \left(\frac{\text{+Profit% - Loss%}}{2} \right) $

[Note: If resulting value is + ve it denotes Profit and – ve it denotes loss.]

Reduced Price = $\displaystyle \frac{{\text{Total Price}} \times {\text {Reduced%}}}{{\text{Extra no of articles}}}$

Increased Price = $\displaystyle \frac{{\text{Total Price}} \times {\text {Increased%}}}{{\text{Less no of articles}}}$

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