#### 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.

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?

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 profit

percentage

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%.

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%?

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.

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.

SP of first article = 125% of CP = Rs.140 CP_{1} =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.

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?

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?

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?

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?

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?

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?

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.

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).