## Profit & Loss

#### 1)A Girl purchases 15 Books for Rs.7500 and she sells each at Rs.575. Find the overall profit or loss percentage.

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CP of 15 Books = Rs.7500, CP of 1 Book = Rs.500
SP of 1 Book = Rs.575
Profit percentage = $${SP-CP \over {CP}}$$ * 100 =  $${575-500 \over {500}}$$ * 100 = 15% Hence (a).

#### 2)Selling price of a pen is Rs.80. If the gain is 11.11%, then what is the cost price of the given pen?

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SP = Rs.80, profit = 11.11%
SP = 111.11% of CP = 80
100% of CP = 72  Hence (b).

#### 3)If the cost price of 30 black boards is equal to selling price of 35 black boards, find loss or profitpercentage

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30 black boards CP = 35 black boards SP
$${SP \over {CP}}$$ =  $${6 \over {7}}$$
Loss % = $${CP - SP \over {CP}}$$ * 100
= $$1-{SP \over {CP}}$$ * 100 =  $$1-{6 \over {7}}$$ * 100 = 14.28% Hence (d).

#### 4)Find a single discount equivalent to three successive discounts of 10%, 25% and 30%.

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Let the CP be Rs.100 10% discount 25% discount 30% discount 100 à90 à 67.5 à 47.25 Single discount = 52.75% Hence (c).

#### 5)If a Bike is sold for Rs.70000, the retailer incurs a loss of 30%. At what price must he sell the Bike in order to gain 17%?

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SP = (1 – L %)CP 70000 = (1 – 30%)CP à CP = 100000 To obtain a gain of 17% SP = (1 + P %)CP SP = (1 + 17%) 100000 = 117000. Hence (b).

#### 6)A dishonest Dealer sells Wheat at cost price. But he sells using false weight and thus gains 9$${6 \over {46}}$$%. Find the weight he uses in place of the 1kg weight of wheat.

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Gain % =  $${Error \over {True value-error}}$$ * 100
$${300 \over {47}}$$ =  $${x \over {1000 - x}}$$ * 100
x = 60 gm
True value = 1000 – x = 1000 – 60 = 940  gm  Hence (c).

#### 7)By selling two articles for Rs.140 each, a dealer gains 25% on one and loses 28.56% on other article. Find the overall profit or loss percentage.

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SP of first article = 125% of CP = Rs.140 CP1 =Rs.112 SP of second article = 71.44% of CP = Rs.140 CP1 =Rs.196 Total CP = 112 + 196 = Rs.308 Total SP = Rs.280 Loss % = $${CP - SP \over {CP}}$$ * 100 = $${308 - 280 \over {308}}$$ * 100 =$${1 \over {11}}$$ * 100à 9.09%Hence (b).

#### 8)A Silver Bracelet was marked at Rs.1800. After two successive discounts, it was sold for Rs.1224. If the first discount was 15%, find the second discount percentage.

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MP of  Silver Bracelet = Rs.1800
After the first 15% discount, price = 1800 – 270 = Rs.1530
Second discount = $${MP-SP \over {SP}}$$ * 100 =  $${1530-1224 \over {1530}}$$ * 100 = 20% Hence (c).

#### 9)The selling price of a Arduino is Rs.2205 after giving two successive discounts of 10% and 12.5%. What is the marked price of the arduino?

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SP =  MP ( 1 -  $${D_{1} \over {100}}$$ )(1 -  $${D_{2} \over {100}}$$ )
2205 =  MP ( 1 -  $${10 \over {100}})$$ (1 -  $${12.5 \over {100}}$$ )
MP = Rs.2800  Hence (d).

#### 10)The selling price of an bouquet is one and one-third times its cost price. If the selling price is 75% of the marked price, what is the mark-up percentage?

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SP = 1.3CP
SP = 75% of MP
1.3CP = 75% of MP = 0.75 MP
$${MP \over {CP}}$$ =  $${1.3 \over {0.75}}$$
MP% = $$({MP \over {CP}}$$ - 1) * 100
= ($${1.3 \over {0.75}}$$ –  1)* 100 = 73.33%  Hence (a).

#### 11) A shopkeeper marked the price of a Furniture at Rs.76000. He offers a 15% discount and also gives a Gift pack worth Rs.1800 along with it. If he receives a profit of 8%, what is the approximate cost price of the Furniture?

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MP of the Furniture = Rs.76000 Discount à 15% SP = 85% of MP = Rs.64600 Let the CP of Furniture be a. and also it includes the 1800 gift pack, CP = a + 1800 Profit 8% SP = 108% of CP = 108% of (a+1800) => 64600 a = Rs.58015(Approximately) Hence (d).

#### 12)  A and B both sell Smartphones which have a marked price of Rs.56000. A gives a discount of 7.14% on the whole, while B gives a discount of 15% on the first Rs.42000 and two-seventh on the rest. By what percentage B’s selling price is approximately less than A’s selling price?

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MP = Rs.56000 SP for A = 92.86% of MP = 92.86% of 56000 = Rs.52000 Discount by B on the first Rs.42000 à 15% SP1 = Rs.35700 Further discount by B on the remaining Rs.14000 à2/7 of the 14000 SP2 = Rs.10000 Total SP for B = 35700 + 10000 = Rs.45700 B’s selling price is less than A’s selling priceby = $${52000-45700 \over {52000}}$$ * 100 = 12%(Approximately)Hence (c).

#### 13)The selling price of a Fitbit band is Rs.2475 after giving three successive discounts of 20%, 8.33% and 25%. What is the marked price of the Fitbit band?

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SP of Fitbit band = Rs.2475
SP = MP (1 - $${D_{1} \over {100}}$$ )(1 -  $${D_{2} \over {100}}$$ ) (1 -  $${D_{3} \over {100}}$$ )
2205 = MP (1 - $${20 \over {100}})$$ (1 -  $${8.33 \over {100}}$$ ) (1 -  $${25 \over {100}}$$ )
2205 = MP (1 -  $${1 \over {5}})$$ (1 -  $${1 \over {12}}$$ ) (1 -  $${1 \over {4}}$$ )
2205 = MP ($${4 \over {5}}$$ ) ( $${11 \over {12}}$$ ) ( $${3 \over {4}}$$ )
MP = Rs.4500  Hence (a).

#### 14) Ravi is a dishonest shopkeeper and uses 925 gm weight instead of 1 kg. His cost price and selling price per kg of grocery items are Rs.48 and Rs.56 respectively. What is his profit percentage if he sells 25kg of the grocery items?

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Shopkeeper uses 925 gm weight instead of 1 kg
So, Gain in weight = 1000 – 925 = 75 gm.
He sells 25 kg, Gain in weight = 25 * 75 = 1875 g.
Actual weight delivered = 25 – 1.875 = 23.125 kg
CP of 23.125 kg = 48 * 23.125 = Rs.1110
SP of 25 kg = 56 * 25 = Rs.1400
Profit % =  $${SP - CP \over {CP}}$$ * 100
= $${1400 - 1110 \over {1110}}$$ * 100
= 26.12% Hence (b).

#### 15) A Business man sells three products, one at a gain of 15%, another at a loss of 30% and the  third at a gain of 40%. If the selling prices of all the three are same, find how much percentage is their average CP lower than or higher than their average SP.

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Let the selling prices of each product be x and cost prices of the three products be p, q and r respectively.
Therefore, Average SP = $${3x \over {3}}$$ = x
CP of first product p= Gain 15%
= x *$${100 \over {115}}$$ =  $${20 \over {23}}$$ x
CP of second product q= Loss 30%
= x *$${100 \over {70}}$$ =  $${10 \over {7}}$$ x
CP of third product r= Gain 40 %
= x *$${100 \over {60}}$$ =  $${5 \over {3}}$$ x
Average CP = $${p+q+r \over {3}}$$
= $${({20x \over {23}})+({10x \over {7}})+({5x \over {3}}) \over {3}}$$
= $${1915x \over {1449}}$$
Here Average CP > Average SP
Required percentage = $${Average CP-Average SP \over {Average SP}}$$ * 100
=$${{1915x \over {1449}} -x \over {x}}$$ * 100
= 32.16% Hence (d).

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