# Profit and Loss Questions

**FACTS AND FORMULAE FOR PROFIT AND LOSS QUESTIONS**

**Selling Price (SP) :*** *The price at which the shopkeeper sells the goods is called the selling price (SP) of the goods sold by the shopkeeper.

**Profit :*** *If the selling price of an article is more than its cost price, then the dealer (or shopkeeper) makes a profit (or gain)

i.e Profit = SP - CP; SP > CP

**Loss :*** *If the selling price of an article is less than its cost price, then the dealer suffers a loss.

i.e loss = CP - SP; CP > SP

**IMPORTANT FORMULAE**

**1. **Profit percentage = $\left(\frac{Profit}{C.P}\times 100\right)$

**2. **Loss percentage = $\left(\frac{Loss}{C.P}\times 100\right)$

**3.$S.P=\left[\frac{100+Gain\%}{100}\times C.P\right]=\left[\frac{100-Loss\%}{100}\times C.P\right]$**

**4. $C.P=\left[\frac{100}{100+Gain\%}\times S.P\right]=\left[\frac{100}{100-Loss\%}\times S.P\right]$ **

**5. **If an article is sold at a gain of say 35%, then SP = 135% of CP

**6. **If an article is sold at a loss of say 35%, then SP = 65% of CP

**7. **When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by :$Loss\%=\left(\frac{CommonLossandGain\%}{10}\right){}^{2}={\left(\frac{x}{10}\right)}^{2}$

**8. **If a trader Professes to sell his goods at cost price, but uses false weihts, then

$Gain\%=\left[\frac{Error}{TrueValue-Error}\times 100\right]\%$

A) No profit, no loss | B) 5% |

C) 8% | D) 10% |

Explanation:

C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.

S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.

Gain =(80/1600*100) % = 5%

A) 16 | B) 18 |

C) 20 | D) 22 |

Explanation:

Let S.P. of 45 lemons be Rs. x.

Then, 80 : 40 = 120 : x or x = $\frac{40\times 120}{80}$= 60

For Rs.60, lemons sold = 45

For Rs.24, lemons sold =$\frac{45}{60}\times 24$= 18.

A) 20% | B) 21% |

C) 22% | D) 23% |

Explanation:

Gain % = $\left(\frac{{\left(100+commongain\%\right)}^{2}}{100}-100\right)$%

=$\left(\frac{{\left(100+10\right)}^{2}}{100}-100\right)$

= 21%

A) 116% | B) 166.66% |

C) 60% | D) 100% |

Explanation:

Let the cost price of 1-liter pure milk be Re.1, then

$\left\{\begin{array}{l}6liters\left(milk\right)\to C.P=Rs.6\\ 2liters\left(water\right)\to C.P=Rs.0\end{array}\right.\to CP=Rs.6only$

8 litre mixture =>

SP => 8 x 2 = Rs. 16

Profit % = $\frac{16-6}{6}x100=\frac{1000}{6}=\mathbf{166}\mathbf{.}\mathbf{66}\mathbf{\%}$

A) Rs. 2000 | B) Rs. 2200 |

C) Rs. 2400 | D) Data inadequate |

Explanation:

Let C.P. be Rs. *x*.

Then,= >$\frac{1920-x}{x}*100=\frac{x-1280}{x}*100$

=> 1920 - *x* = *x* - 1280

=> 2*x* = 3200

*=> x* = 1600

Required S.P. = 125% of Rs. 1600 =Rs(125/100*1600) = Rs2000

A) 12% | B) 30% |

C) 50% | D) 60% |

Explanation:

Friends, we know we will need gain amount to get gain percent, right. So lets get gain first.

Let the cost price of 1 pen is Re 1

Cost of 8 pens = Rs 8

Selling price of 8 pens = 12

Gain = 12 - 8 = 4

Gain% = $\left(\frac{gain}{\mathrm{cos}t}\times 100\right)$% = $\left(\frac{4}{8}\times 100\right)$% = 50%

A) 15 | B) 16 |

C) 18 | D) 25 |

Explanation:

Let C.P. of each article be Re. 1 C.P. of *x* articles = Rs. *x*.

S.P. of *x* articles = Rs. 20.

Profit = Rs. (20 - *x*).

$\left(\frac{20-x}{x}*100=25\right)$

=> 2000 - 100*x* = 25*x*

=> 125x=2000

=> x=16

A) 600 | B) 1200 |

C) 1800 | D) none of these |

Explanation:

Least Cost Price = Rs. (200 * 8) = Rs. 1600.

Greatest Selling Price = Rs. (425 * 8) = Rs. 3400.

Required profit = Rs. (3400 - 1600) = Rs. 1800.