# Profit and Loss

1. A dealer marks his goods 20% above cost price.  He then allows some discount on it and makes a profit of 8%. The rate of discount is :
 a. 12% b. 10% c. 6% d. 4%
Correct Option : B
Explanation:
Let C.P.=Rs.100
Marked price = Rs.120, S.P. = Rs.108
Discount = $\left[ {\displaystyle\frac{{12}}{{120}} \times 100} \right]$% = 10%

2. A cloth merchant has announced 50% rebate in prices. If one needs to have a rebate of Rs.40, then how many shirts, cash costing Rs.32, he should purchase ?
 a. 6 b. 5 c. 10 d. 7
Correct Option : B
Explanation:
Suppose the number of shirts = x.
Then, rebate = $\left[ {\displaystyle\frac{{25}}{{100}} \times 32x} \right] = 8x$
8x=40 or x = 5.

3. The price of an article was increased by p%. Later the new price was decreased by p%. If the latest price was Rs.1, the original price was :
 a. Rs. 1 b. $\left[ {\displaystyle\frac{{1 - {p^2}}}{{100}}} \right]$ c. $\left[ {\displaystyle\frac{{10000}}{{10000 - {p^2}}}} \right]$ d. $\left[ {\sqrt {\displaystyle\frac{{1 - {p^2}}}{{100}}} } \right]$
Correct Option : C
Explanation:
Let the original price = Rs.x
Price after P% increase = (100+P)% of x
=$\displaystyle\frac{{(100 + P)x}}{{100}}$
New price after P% decrease
= (100-P)% of $\left[ {\displaystyle\frac{{(100 + P)x}}{{100}}} \right]$
= $\displaystyle\frac{{(100 - P)}}{{100}} \times \displaystyle\frac{{(100 + P)}}{{100}} \times x$
= $\displaystyle\frac{{(100 - P)(100 + P)}}{{100 \times 100}} \times x = 1$
or x = $\displaystyle\frac{{100 \times 100}}{{(100 - P)(100 + P)}} = \displaystyle\frac{{10000}}{{10000 - {P^2}}}$

4. The difference between a discount of 40% on Rs.500 and two successive discount of 36%  and 4% on the same amount is :
 a. 0 b. Rs.2 c. Rs.1.93 d. Rs.7.20
Correct Option : D
Explanation:
Sale after 40% discount = 60% of Rs.500
=Rs.300. Price after 36% discount = 64% of Rs.500=Rs.320.
Price afdter next 4% discount = 96% of Rs.320 = Rs.307.20
Difference in two prices = Rs.7.20

5. Tarun bought a T.V with 20% discount on the labelled price. Had he bought it with 50% discount, he would have saved Rs.500. At what price did he buy the T.V ?
 a. Rs.5000 b. Rs.10,000 c. Rs.12000 d. Rs.6000
Correct Option : B
Explanation:
Let the labelled price be Rs.100, S.P in Ist case = Rs.80, S.P in 2nd case = Rs.75. If saving is Rs.5, labelled price
= Rs.$\left[ {\displaystyle\frac{{(100}}{5} \times 500} \right]$
= Rs.10000

6. A man purchases an electric heater whose printed price is Rs.160. If he received two successive discounts of 20% and 10%; he paid :
 a. Rs.112 b. Rs.129.60 c. Rs.119.60 d. Rs.115.60
Correct Option : D
Explanation:
Price after Ist discount = 100% of Rs.160 = Rs. 128
Price after 2nd discount = 90% of Rs.128 = Rs.115.20

7. The marked price is 10% higher than the cost price.  A discount of 10% is given on the marked price. In this kind of sale, the seller
 a. bears no loss, no gain b. gains c. losses d. None of these
Correct Option : C
Explanation:
Let C.P = Rs.100
Marked price = Rs.110
S.P = 90 % of Rs.110 = Rs.99
Loss = 1%

8. A trader lists his articles 20% above C.P and allows a discount of 10% on cash payment.  His gain percent is :
 a. 10% b. 8% c. 6% d. 5%
Correct Option : B
Explanation:
Let C.P = Rs.100
Then, marked price = Rs.120
S.P = 90% of Rs.120= Rs.108
Gain = 8%

9. While selling a watch, a shop-keeper gives a discount of 5%. If he gives a discount of 7%, he earns Rs.15 less as profit. The marked price of the watch is :
 a. Rs.697.50 b. Rs.712.50 c. Rs.787.50 d. None of these
Correct Option : D
Explanation:
Let the marked price be Rs. x
Then (7% of x ) - 15 = 5% of x
or $\displaystyle\frac{{7x}}{{100}} - \displaystyle\frac{{5x}}{{100}} = 15$ or x =750

10.A shop-keeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is :
 a. 45 : 56 b. 50 : 61 c. 99 : 125 d. None of these
Correct Option : A
Explanation:
Let the printed price of the book be Rs.100. After a discount of 10% S.P= Rs.90 Profit earned = 12%
C.P. of the book =
Rs. $\left[ {\displaystyle\frac{{100}}{{112}} \times 90} \right]$=Rs.$\displaystyle\frac{{1125}}{{14}}$
Hence, (C.P) : (printed price)=$\displaystyle\frac{{1125}}{{14}}$:100
or 45:56

11.A retailer buys a sewing machine at a discount of 15% and sells it for Rs.1955. Thus he makes a profit of 15%. The discount is :
 a. Rs.270 b. Rs.290 c. Rs.300 d. None of these
Correct Option : C
Explanation:
Cost price for the retailer = $\displaystyle\frac{{100}}{{(100 + 15)}} \times 1955 = 1700$
But this price is what retailer got after having got a discount of 15%.
Let the marked price be Rs.x . Purchase price by the retailer = (100-15)% of Rs.x.
So $\displaystyle\frac{{85}}{{100}} \times x = 1700 \Rightarrow x = 2000$
= (15% of Rs.2000) = Rs.300

12.An umbrella marked at Rs.80 is sold for Rs.68. The rate of discount is :
 a. 15% b. 12% c. $17\displaystyle\frac{{11}}{{17}}$% d. 20%
Correct Option : A
Explanation :
Discount = $\left[ {\displaystyle\frac{{12}}{{80}} \times 100} \right]$%=15%

13.Kabir buys an article with 50% discount on its marked price.  He makes a profit of 10% by selling it at Rs.660.  The marked price is :
 a. Rs.600 b. Rs.700 c. Rs.800 d. 685
Correct Option : C
Explanation:
Cost price for Kabir = $\displaystyle\frac{{100}}{{100 + 10}} \times 660 = 600$
But this price is what he got after having a discount of 50%. Let the marked price be x.
Then (100 - 25)% of x = 600 $\Rightarrow$ x = Rs.800

Alternatively:
Let the original price be Rs.x
C.P = (x - 50% of x ) = $\displaystyle\frac{{3x}}{4}$
S.P = $\left[ {\displaystyle\frac{{3x}}{4} + 10\% {\rm\text{ of }}\displaystyle\frac{{3x}}{4}} \right] = \displaystyle\frac{{33x}}{{40}}$
$\displaystyle\frac{{33x}}{{40}}$=660$\Rightarrow$x=800

14.The ratio of the prices of three different types of cars is 4:5:7. If the difference between the costliest and the cheapest cars is Rs.60000, the price of the car of modest price is :
 a. Rs.80000 b. Rs.100000 c. Rs.140000 d. Rs.120000
Correct Option : B
Explanation:
Let the price be 4x, 5x and 7x rupees.
Then, 7x-4x=60000 $\Rightarrow$ x=20000.
Required price = 5x=Rs.100000.

15.A discount series of 10%, 20% and 40% is equal to a single discount of :
 a. 50% b. 56.8% c. 60% d. 70.28%
Correct Option : B
Explanation:
Let original price = Rs.100. Price after first discount = Rs.90. Price after second discount
= Rs. $\left[ {\displaystyle\frac{{80}}{{100}} \times 90} \right]$=Rs.72
Price after third discount = Rs.$\left[ {\displaystyle\frac{{60}}{{100}} \times 72} \right]$
= Rs.43.20
Single discount = (100-43.20)=56.8%

16. Subhash purchased a tape recorder at $\displaystyle\frac{9}{{10}}th$ of its selling price and sold it at 8% more than its S.P. His gain is :
 a. 8% b. 10% c. 18% d. 20%
Correct Option : D
Explanation:
Let the S.P be Rs.x
Then, C.P paid by Subhash = Rs.${\displaystyle\frac{{9x}}{{10}}}$
S.P. received by Subhash = (108% of Rs.x)
= Rs.${\displaystyle\frac{{27x}}{{25}}}$
Gain = Rs.$\left[ {\displaystyle\frac{{27x}}{{25}} - \displaystyle\frac{{9x}}{{10}}} \right]$=Rs.$\displaystyle\frac{{9x}}{{50}}$
Hence Gain % =$\left[ {\displaystyle\frac{{9x}}{{50}} \times \displaystyle\frac{{10}}{{9x}} \times 100} \right]$% = 20%

Alternatively:
Assume Selling price is 100. So he gets it for 90.  and sold it for 108. His profit is 18. Profit percentage is 18/90 x 100 = 20%
Easy. is it not!!

17.At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ?
 a. Rs.7.50 per kg b. Rs.8.20 per kg c. Rs.8.85 per kg d. Rs.9 per kg.
Correct Option : D
Explanation:
Total C.P of 200 kg of sugar
= Rs.$(80 \times 6.75 + 120 \times 8)$=Rs.1500
C.P of 1 kg = Rs.$\left[ {\displaystyle\frac{{1500}}{{200}}} \right]$=Rs.7.50
Gain required = 20%
S.P of 1 kg = (120% of Rs.7.50)
= Rs.$\left[ {\displaystyle\frac{{120}}{{100}} \times 7.50} \right]$=Rs.9 per kg.

18.A person bought an article and sold it at a loss of 10%.  If he had bought it for 20% less and sold it for Rs.55 more, he would have had a profit of 40%. The C.P.of the article is :
 a. Rs.200 b. Rs.225 c. Rs.250 d. None of these
Correct Option : C
Explanation:
Let C.P = Rs.x. Then S.P = Rs.$\left[ {\displaystyle\frac{{90}}{{100}} \times x} \right]$ = Rs.$\left[ {\displaystyle\frac{9}{{10}}x} \right]$
New C.P = Rs.$\left[ {\displaystyle\frac{{80}}{{100}} \times x} \right]$=Rs.$\left[ {\displaystyle\frac{{4x}}{5}} \right]$
Now gain = 40%
New S.P = $\left[ {\displaystyle\frac{{140}}{{100}} \times \displaystyle\frac{{4x}}{5}} \right]$=Rs.$\left[ {\displaystyle\frac{{28}}{{25}}x} \right]$
${\displaystyle\frac{{28}}{{25}}x - \displaystyle\frac{9}{{10}}x = 55}$ or x = 250
Hence, C.P = Rs.250

Alternatively:
Assume Cost price is 100x. Then initial selling price is 90x (Why? 10% loss!)
Had he bought it for 20% less, then his cost price be 80x
Now on this 80x, he got a profit percentage of 40%. So new selling price is 140% (80x) = 112x
But the difference in selling prices is 55. So 112x - 90x = 22x = 55 $\Rightarrow$ x = 5/2
Substituting this value in 100x we get cost price = Rs.250

19.The cost price of an article, which on being sold at a gain of 12% yields Rs.6 more than when it is sold at a loss of 12% is :
 a. Rs.30 b. Rs.25 c. Rs.24 d. Rs.20
Correct Option : B
Explanation:
Let C.P = Rs.x. Then ${\displaystyle\frac{{112}}{{100}}x - \displaystyle\frac{{88}}{{100}}x = 6}$
or 24x = 600 or x =${\displaystyle\frac{{600}}{{24}} = 25}$
C.P = Rs.25

20. A man sells a car to his friend at 10% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :
 a. Rs.25000 b. Rs.37500 c. Rs.50000 d. Rs.60000
Correct Option : C
Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.$\left[ {\displaystyle\frac{{100}}{{120}} \times 54000} \right]$=Rs. 45000
This is the price the first person sold to the second at at loss of 10%.
Now S.P = Rs.45000 and loss = 10%
C.P. Rs.$\left[ {\displaystyle\frac{{100}}{{90}} \times 45000} \right]$= Rs.50000.

21.  Bhajan Singh purchased 120 reams of paper at Rs.80 per ream. He spent Rs.280 on transportation, paid octroi at the rate of 40 paise per ream and paid Rs.72 to the coolie. If he wants to have a gain of 8% , what must be the selling price per ream ?
 a. Rs.86 b. Rs.87.48 c. Rs.89 d. Rs.90
Correct Option : D
Explanation:
C.P of 120 reams = Rs.$(120 \times 80 + 280 + 72 + 120 \times 0.40)$= Rs.10000.
C.P. of 1 ream = ${\displaystyle\frac{{10000}}{{120}}}$= Rs.${\displaystyle\frac{{250}}{3}}$
S.P. of 1 ream = Rs.${\displaystyle\frac{{108}}{{100}} \times \displaystyle\frac{{250}}{3} = }$Rs.90

22. Of two mixers and one T.V cost Rs.7000, while two T.Vs and one mixer cost Rs.9800, the value of one T.V is :

 a. Rs.2800 b. Rs.2100 c. Rs.4200 d. Rs.8400
Correct Option : C
Explanation:
2x+y = 7000    ............  (i)
x+2y=  9800    ..............(ii)
Solving (i) and (ii), we get y = 4200

23. Profit after selling a commodity for Rs.425 is same as loss after selling it for Rs.355. The cost of the commodity is :

 a. Rs.385 b. Rs.390 c. Rs.395 d. Rs.400
Correct Option : B
Explanation:
Let C.P = Rs.x. Then.
425-x= x-355 or 2x = 780 or x = 390.

24.  A merchant sold his goods for Rs.75 at a profit percent equal to C.P. The C.P was :

 a. Rs.40 b. Rs.50 c. Rs.60 d. Rs.70
Correct Option : B
Explanation:
Let C.P=Rs.x
x + x% of x = 75 or x + ${\displaystyle\frac{{{x^2}}}{{100}}}$=75 or
${{x^2} + 100x - 7500 = 0}$ or (x + 150)(x-50)=0
x = 50 (Neglecting x = - 150)

25. A horse and cow were sold for Rs.12000 each. The horse was sold at a loss of 20% and the cow at a gain of 20%. The entire transaction resulted in :

 a. No loss or gain b. Loss of Rs.1000 c. Gain of Rs.1000 d. Gain of Rs.2000
Correct Option : B
Explanation:
In the special case of profit and loss percentages are equal and Selling price is same, then the transaction always results in Loss. This loss percentage is given by a simple formula $- {\left( {\displaystyle\frac{x}{{10}}} \right)^2}$
So in this case, Profit% = Loss% = 20. So x = 20
Loss percentage = $- {\left( {\displaystyle\frac{{20}}{{10}}} \right)^2} = - 4$
Total S.P = Rs.24000
Cost price = $24000 \times \displaystyle\frac{{100}}{{96}}$ = 25000
Loss = Rs.1000