Profit & Loss

1. A retailer gets a discount of 40 % on the printed price of an article. The retailer sells it at the printed price. His gain percent is

(a) 40                                     (b) 55

(c) 66  \frac{2}{3}                                 (d) 75

Solution: (c)

 $P\%=\frac{40}{60}\times 100=66\frac{2}{3}\%$

2. If the cost price of 25 pens is equal to the selling price of 20 pens, then profit percent is

(a) 20 %                                (b) 25 %

(c) 15.5   %                               (d) 5 %

Solution: (b) C.P of 25 pen = S.P of 20 pen

\frac{cp}{sp}=\frac{20}{25}=\frac{4}{5}>1= profit

Profit% =\frac{1}{4}\times 100=25\%

3. A dealer marks a washing machine for ₹ 7,500, and allows a discount of 6 % on it. Find the selling price

(a) 6850                                (b) 7050

(c) 7250                                (d) 6950

Solution: (b)   6\%=\frac{3}{50}(\frac{discount}{MP})

SP = 50-3=47

MP\to 50 unit = Rs. 7500

So, SP\to 47 unit = Rs. 7050

4. The marked price of an article is 30 % higher than the cost price. If a trader sells the articles allowing 10 % discount to customer, then the gain p will be

(a) 17                     (b) 20

(c) 19                     (d) 15

Solution:

Now profit% = \frac{117-100}{100}\times 100=17\%

5. A merchant marked the price of an article by increase its production cost by 40 %. Now he allows 20% discount and gets a profit of Rs.48 after selling it. The production cost is

(a) Rs.320                            (b) Rs.360

(c) Rs.400                             (d) Rs.440

Solution: (c)

Profit = 112-100 =12 unit

12 unit = ₹ 48

1 unit = ₹ 4

So, C.P = 100 unit = ₹ 400

6. A watch dealer pays 10 % customs duty on a watch which cost Rs. 500 aboard. He desires to make a profit of 20 % after giving discount of 25 % to the buyer. The marked price should be

(a) Rs. 950                           (b) Rs. 800

(c) Rs. 880                            (d) Rs. 660

Solution: (c) C.P = 500+10% of 500

 =\frac{CP}{MP}=\frac{100-discount\%}{100+Profit\%}=\frac{100-25}{100+20}

\frac{CP}{MP}=\frac{75}{120}=\frac{5}{8}

MP= 8 unit= 8\times 110=880 Rs

7. A shopkeeper allows 25 % discount on his advertised price and to make a profit 25 % on his outlay.What is the advertised price (in Rs. ) on which he gains Rs . 6000?

(a)36000                               (b) 4000

(c) 39000                              (d) 42500

Solution: (b) let C.P = 100

Profit = 125-100=25 unit

MP=MP = $x=\frac{75}{100}=125

MPMP$=x=\frac{500}{3}unit

$=\frac{500}{3}\times \frac{6000}{25}=40,000$

8. If the profit on selling an article for Rs. 452 is the same as the loss on selling it for Rs. 355, then the cost price of the article is

(a) Rs.410                            (b) Rs.380

(c) Rs.400                             (d) Rs.390

Solution: (d)

So, 2x = 425-355

2x= 70

X=35

C.P = 255+35=390

9. A & B jointly made a profit of Rs.1650 and they decided to share it such that 1/3 of a’s profit is equal to 2/5 of B’s profit. Then profit of B is

(a) Rs.700                            (b) Rs.750

(c) Rs.850                             (d) Rs.800

Solution: (b) According to the questions

$A\times \frac{1}{3}=B\times \frac{2}{5}$

\frac{A}{B}=\frac{6}{5}  (profit ratio)

Total profit = 6+5= 11 unit

Therefore, 11 unit = ₹ 1650

1 unit = ₹ 150

Profit of B = 5 unit

$=5\times 150=750$

10. 4% of the selling price of an article is equal to 5% of its cost price , Again 20% of the selling price is Rs. 120 more than 22% of its cost price. The ratio of cost price & selling price is

(a) 2 : 3                                 (b) 3 : 2

(c) 4 : 5                                 (d) 5 : 4

Solution: (c) According to the questions

$SP\times \frac{4}{100}=CP\times \frac{5}{100}$

$\frac{CP}{SP}=\frac{4}{5}$

11. Due to 25% fall in the rate of eggs one can buy 2 dozen eggs more than before by investing Rs. 162 . The original rate per dozen of the eggs is

(a).Rs. 22                             (b) Rs. 24

(c). Rs. 27                             (d) Rs. 30

Solution: (c) 25% Fall we get 2 dozen eggs extra

Therefore, 25%= 2 dozen

100%=8 dozen(new quantity)

So, Old quanity = 8-2=6 dozen

Rate = \frac{162}{6}= Rs. 27

12. Last year Mr. A bought two paintings. This year he sold them for Rs. 20,000 each. On one, he made a 25% profit and of the other he had a 25% loss . Then his net profit or loss is

(a). He lost more than Rs. 2000

(b) He lost more than Rs. 2000

(c) He earned more than Rs. 2000

(d) he earned less than Rs. 2000

13. A shopkeeper sells rice at 10% profit and users weight 30% less the actual measure. His gain percent is

14. A photographer allows a discount of 10% on the advertised price of a camera. The price (in ₹) that must be marked on the camera, which cost him ₹ 600 to make a profit of 20% would be

(a). 60                   (b) 800

(c) 700                   (d) 850

Solution: (b) According  to question

15. A dinner set is quoted for ₹ 1500 a customer pays ₹ 1173 for it. If the customer get a series of two discounts and the rate of first discount is 15% then the rate of second discount was

(a). 15%                                (b) 7%

(c) 9%                                   (d) 8%

16. A dishonest dealer defrauds to the extent of x% in buying as well as selling is goods by using faulty weight. What will be the gain percent on his outlay?

17. The ratio of cost price and selling price of an article is 20 : 21 . The gain percent on it is

(a)4                       (b) 5

(c)6                        (d)10

Solution: (b) according to question

\frac{CP}{SP}=\frac{20}{21}

Profit% = =\frac{1}{20}\times100=5%

18. The ratio of cost price and selling price is 25:26. The percent of profit will be

(a) 26 %                                (b) 25 %

(c) 1 %                                   (d) 4 %

Solution: (d) According to question

\frac{CP}{SP}  =\frac{25}{26}

Profit = SP-CP = 26-25=1

Profit%  =\frac{1}{25}\times100=4%

19. A shopkeeper buys a product of ₹ 150 per kg . 15% of product was damaged. At what price (per kg) should he sell the remaining so as to earn a profit of 20 %?

20. Mr. Kapoor purchased two toy cycles for ₹ 750 each. He sold these cycles, gaining 6 % on one and losing 4 % on the other. The gain of loss percent in the whole transaction  is

(a) 1 % loss                          (b) 1 % gain

(c) 1.5% loss                       (d ) 1.5 % gain

21. The profit earned by a shopkeeper by selling a bucket at a gain of 8 % is ₹ 28 more then when he sells it at a loss of 8 %. The cost price (in rupees) of the bucket is

(a) 170                                  (b ) 190

(c) 175                                   (d) 165

Solution: (c)

16 unit = 28

1 unit = \frac{28}{16}

C.P= 100 unit = \frac{28}{16}\times100 = Rs. 175

22. Man bought 500 meter of electric wire at 50 paise per meter ,he sold 50 % part at the profit of 5 %, at what % profit he sold remaining as to gain 10 % on the whole transaction?

(a) 13%                                                 (b) 12.5 %

(c) 15 %                                                (d) 20%

Solution: (c) Using Allegation
Let he sell remaining at x%

(x-10)/5=250/250x = 15%

23. A book seller allowed 10 % discount on printed price. He gets 30 % commission from publisher. His profit in percent will be

(a) 20                                     (b) 28\frac{4}{7}

(c)25                                      (d)28\frac{3}{7}

Solution:

Profit = MP (9) – SP (7)

\frac{2}{7}\times100=28\frac{4}{7}%

24. A dealer is selling an article at a discount of 5 % on the marked price. If the marked price is 12 % above the cost price and the article was sold for ₹ 532 then the cost price is (in ₹)

(a) 500                                  (b) 525

(c) 505                                   (d) 520

Solution: (a)Let C.P of the article be Rs. x

Therefore, M.P= Rs. \frac{112x}{100}

Now,

\frac{112x}{100} \times\frac{95}{100} = 532

\frac{532\times10000}{112\times95}

= Rs. 500

25. A shopkeeper increase the price of an object by 40% and then sells it at 25 % discount on the marked price .if the selling price of such an object be ₹ 2100, its cost price for the shopkeeper was?

(a) 3000                                (b) 1500

(c) 1750                                (d) 2000

Solution: (d)  let CP of the articles is 100

So, MP = 140% of 100

\Rightarrow\frac{140}{100}\times100=140

Now , give 25% discount

So, SP = 140-25% of 140

\Rightarrow140-\frac{1}4{}\times140=105

105 \rightarrow 2100

\rightarrow 20

100 \rightarrow 20 \times 100 = ₹ 2000

26. By what fraction selling price (S.P.) MUST be multiplied to get the cost price (C.P) if the loss is 20 %?

(a) \frac{4}{5}                                        (b) \frac{8}{5}

(c)  \frac{5}{4}                                      (d) \frac{6}{5}

Solution: (c)  % loss = 20%

20% = \frac{1}{5}

It CP= 5 units

Loss = 1 unit

SP = 5-1 = 4 unit

We make it equal to CP that is (5)

So we multiply SP by = \frac{5}{4}

S.P = 4\times\frac{5}{4}=5

27. Ramesh sold a book at a loss of 30%. If he has sold it for ₹ 140 more, he would have made a profit of 40%. The cost price of the book is

(a). ₹ 280                             (b) ₹ 200

(c) ₹ 260                               (d) ₹ 300

Solution: (b)   140= (40-(-30))%

140 = (40+30)%

140=70%

\frac{140\times100}{70} = 200

or,

70% \to 140

1 % \to 2

100 % \to\times 100 = ₹ 200

28. A shopkeeper purchased 510 eggs at the rate of ₹ 20 per dozen. 30 eggs were broken on the way. In order to make a gain of 20%, he must sell the remaining eggs at the rate of

(a).₹ 22.50 per dozen

(b) ₹ 25.50 per dozen

(c)₹ 26 per dozen

(d) ₹ 26.50 per dozen

Solution: (b) total price of 510 Eggs

Dozen price = ₹ 20

Price of 510 eggs = \frac{510}{12}\times20 =850

Gain is 20%

So gain is = \frac{20}{100}\times850 =170

So, SP = 850 + 170 = ₹ 1020

30 eggs are broken = 510- 30 = 480

Per dozen SP = \frac{1020}{480}\times12 =25.50 Rs.

29. A sells a watch to B and makes a loss of 12%. B makes a profit of 12\frac{1}{2} % by selling the watch to c. If a sells he watch to be at the cost of which c purchased it then the percentage of loss or profit of A will be

(a). 1% loss                         (b) 1% profit

(c) 2% loss                           (d) 2% profit

Solution:  (b)

Let the C.P of A be Rs. 100

A sells at 12% loss to B = (100-12)=88

Therefore, C.P. of B =88

B sells at 12.5% Profit to C = (88 +11)=99

Therefore, C.P of C =99

Requires loss percent

\frac{100-99}{100}\times100=1%

30. A man buys 3 type-1 cakes and 6 types-II cakes for ₹ 900. He sells type-I cakes at a profit of 15% and type-II cakes at a loss of 10%. If his overall profits is ₹ 30, the cost price (in ₹) of a type-I and of a type-II cakes is

(a). 100,100                         (b) 160,70

(c) 180, 60                            (d) 120, 90

Solution: (b)

Let the C.P of each cake of type-I be Rs. x and that of type II. be Rs y.

Therefore 3x+6y=900

x+2y=300…..(1)

Again,

3x \times\frac{115}{100}+6y \times\frac{90}{100}=930

115x+180y=31000………….(2)

Solving (1) & (2), we get

y= Rs. 70 , x= Rs. 160

 

 

 

 

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