Profit and loss-part-9

Problems on marked price and discount

Important formula

discount % = \frac{Discount}{MRP}\times 100

Profit %=M-D-\frac{M\times D}{100}

Problem 1: If the marked price of an article is 20% more than its C.P and the shopkeeper allow a discount of 10%. Find his profit percent?

Solution: Profit %=M-D-\frac{M\times D}{100}

=20-10-\frac{20\times 10}{100}

=8%

Problem 2: Saurabh sells an item at 12.5%  profit also he used a false weight of  900 grams at place of 1100 grams. Find his over all profit percentage?

Solution :1100-900=200

p1 =  \frac{200}{900}\times 100=\frac{200}{9}%

p2=12.5%

p1+p2=p

p1+p2+\frac{p1\times p2}{100}

12.5+\frac{200}{9}+\frac{200}{9}\times \frac{12.5}{100}

12.5+\frac{200}{9}+\frac{25}{9}

12.5+25=37.5

Problem 3: A man sold a book at a profit of 10% if he had charged RS 45 more his profit percent would have been 25% .Find the value of X if the average of C.P, 52 and X is 172?

Solution: p1=10%      p2=25%

25%-10%=15%

15%   \rightarrow    45

100%  \rightarrow  ?

\frac{45\times 100}{15}=300

\frac{300+52+x}{3}=172

x=516-352=RS 164

Problem 4: Raju marked the price of an article 25% above the C.P and allowed two successive discount of 15% and 24% respectively as a result he incurred a loss of RS.1078. At what price did he sell the item?

Solution :

C.P             M.R.P      15%,24% Discount

100   \rightarrow    125    \rightarrow 125\times \frac{85}{100}\times \frac{76}{100} =80.75%

100-80.75=19.25

19.25  \rightarrow   1078

100    \rightarrow    ?

\frac{1078\times 100}{19.25}=5600

C.P=5600

S.P=5600-1078=4522

Problem 5:The ratio of C.P to the selling price of an article is 5:6. If 20% discount is offered on marked price of an article the marked price is what percent more than the C.P?

Solution:    C.P               S.P

5       :           6

20% discount is offered =\frac{1}{5}

M.R.P               S.P

5                         4

Selling price should be equal so multiply by 2 in first condition and multiply by 3 in second condition.

C.P               S.P                                                        C.P                    S.P

(5       :           6)*2                     \rightarrow                              10                    12

M.R.P               S.P                                                  M.R.P                S.P

(5                         4)*3                 \rightarrow                           15                   12

\frac{5}{10}\times 100=50%

 

Profit and loss-part-8

Problem 1: A shopkeeper sells an article for RS 350 and gives 2 articles free on purchase of 5 articles. If he still makes a profit of 25%. Find the C.P of each article?

Solution: 25%\rightarrow\frac{1}{4}

2+5=7      1\rightarrowC.P in the below equation

\frac{7\times 1\times 5}{4}= 5\times S.P

S.P=\frac{7}{4}

\frac{7}{4} \rightarrow RS 350

1 \rightarrow ?

350\times \frac{4}{7}=200

Problem 2: A man bought a no.of oranges at 3 for a rupee and an equal number at 2 for a rupee. At what price per dozen should he sell them to make a profit of 20%?

Solution :  3 oranges \rightarrow  RS 1

2 oranges \rightarrow RS 1

Equate oranges

2*3 oranges \rightarrow  RS 1*2             6 oranges \rightarrow RS 2

3*2 oranges \rightarrow RS 1*3              6 oranges \rightarrow RS 3

Total 12 oranges RS 5

12 \rightarrow 5

At what price per dozen should he sell them to make a profit of 20%

20%=\frac{1}{5}

1+5=6

5*\frac{6}{5}  =  RS 6

Problem 3: By selling 45 pens for RS 40, A man losses 20%. How many pen should he sell for RS.24 to gain 20%?

Solution: By selling 45 pens for RS 40, A man losses 20%

\frac{40\times 100}{80}=50

\frac{50\times 120}{100}=RS.60

RS.60  \rightarrow  45 Pens

RS.24  \rightarrow  ?

\frac{45\times 24}{60}= RS.18

Problem 4: Sachin purchased 20 dozen oranges at RS 50 per dozen. He sold 13 dozen at 20% profit and the remaining 7 dozen at 70% profit. What is his over all profit percentage?

Solution: C.P=20*50=1000

=\frac{13\times 50\times 20}{100}+\frac{7\times 50\times 70}{100}

=130+245=375

=\frac{375}{1000}\times 100=37.5

Problem 5: If two shop keeper claims a profit of 25% on same goods but one on the C.P and the other on S.P and the difference in their profit earned by them is RS 100. Find the S.P of good if the S.P is same for both?

Solution :25%=\frac{1}{4}

C.P              S.P

4                  5

3                  4

According to the problem S.P is equal

C.P              S.P

(4                5)*4

(3                4)*5

Profit earned=RS 100

1 \rightarrow 100

C.P           S.P

16               20

15                20

Selling price=20*100=2000

 

Profit and loss-part-7

Problem 1: Mukesh  purchased some banana at the rate of RS 240/100. If he wants to get a profit percent of 12.5%, Find the price of banana per dozen?

Solution : 12.5%  =  \frac{1}{8}

12.5 % profit =1+8=9

100  bananas    \rightarrow     240

1   banana     \rightarrow     ?

\frac{240\times 1}{100}=2.4

The price of banana per dozen =  \frac{2.4\times 12\times 9}{8}=32.4 RS

Problem 2: Rani purchases oranges at RS 10 per dozen and sells them at RS 12 for every 10 oranges. What is the profit percent?

Solution: 12 oranges \rightarrow  RS.10

10 oranges  \rightarrow  RS. 12

cross multiply

Selling price =12*12=144

Cost price =10*10=100

profit or gain percent=  (\frac{Gain\times 100}{C.P})

=\frac{44\times 100}{100}=44%

Problem 3: A shopkeeper sells an item at 16\tfrac{2}{3}% profit. Due to inflation cost price of article is increased by 25%. By how much percent shopkeeper should increase the C.P of an article so that now he may get the profit of 20%?

Solution :   16\tfrac{2}{3}%=\frac{1}{6}

C.P             S.P           Profit

6                   7               1

Cost price is increased by 25%

25%=\frac{1}{4}

6\times \frac{1}{4}=1.5

6+1.5=7.5

get a profit of 20%=\frac{1}{5}

7.5\times \frac{1}{5}=1.5

7.5+1.5=9

By how much percent should increase the C.P

C.P             S.P           Profit

6                   7               1

7.5                9              1.5

7-9=2

\frac{2}{7}\times 100=28\tfrac{4}{7}%

Problem 4: A fruit seller buys some oranges at the rate of 4 for RS 10 and an equal number more at 5 for RS10. He sells the whole lot at 9 for RS 20. What is his loss or gain percent?

Solution :  4 oranges \rightarrowRS.10

5 oranges \rightarrowRS.10

9 oranges \rightarrowRS 20

L.C.M of 4,5,9 is 180

45*4 oranges \rightarrowRS.10*45

36*5 oranges \rightarrowRS.10*36

20*9 oranges \rightarrowRS 20*20

180 oranges \rightarrow450

180 oranges\rightarrow360

180 oranges\rightarrow400

A fruit seller buys some oranges at the rate of 4 for RS 10 and an equal number more at 5 for RS10

360\rightarrow810

He sells the whole lot at 9 for RS 20

360\rightarrow800

810-800=10

\frac{10}{810}\times 100=\frac{100}{81}=1.23% loss

 

Profit and loss-part-6

Problem 1: Rajesh sells  an article at 12.5% profit. If the cost price of an article is decreased by 25% and S.P also decreased by RS 90 new profit percentage becomes 20%. Find the original S.P of an article?

Solution : 12.5%=\frac{1}{8}

C.P                             S.P                     Profit

8                                   9                            +1

The C.P of an article is decreased by 25%

25%=\frac{1}{4}

8\times \frac{1}{4}=2

8-2=6

The new profit becomes 20%

20%=\frac{1}{5}

6\times \frac{1}{5}=1.2

6+1.2=72

9-7.2=1.8

1.8   \rightarrow  90

9      \rightarrow  ?

\frac{90\times 9}{1.8}=450

Problem 2:A vendor sold a smart phone at profit 25% on the S.P. If the selling price of  the smart phone is 1500 more than the profit earned, Find the cost price is how much more than the profit earned by vendor?

Solution : 25% profit on selling price = \frac{1}{4}

25%=\frac{1}{4}

S.P                  C.P                  Profit

4                       3                          1

If the selling price of  the smart phone is 1500 more than the profit earned.

4-1=3

3    \rightarrow     1500

2   \rightarrow      ?(3-1=2)

\frac{1500\times 2}{3}=1000

Problem 3: The total price of the watches is RS.840. One watch is sold on the profit of 16% and other on 12% loss there is no profit and no loss on the whole transaction. Find the C.P of both the watches?

Solution : CP1+CP2=840

= \frac{X\times 16}{100}=\frac{Y\times 12}{100}

=\frac{X}{Y}= \frac{3}{4}

(3+4)7   \rightarrow    840

3   \rightarrow    ?   360

4   \rightarrow     ?

\frac{840\times 3}{7}=360

\frac{840\times4}{7}=480

Problem 3: The S.P of an article A is RS. 1120. The C.P Of another  article B is 20% more than the C.P of article A. If the profit percentage on article A and article B is 40% and 35% respectively then find the S.P of article B?

Solution: C.P_{A}=100          C.P_{B}=120

the profit percentage on article A and article B is 40% and 35%

S.P_{A}=140           S.P_{B}=120\times \frac{35}{100}=42

S.P_{B}  =120+42=162

140  \rightarrow   1120

162  \rightarrow  ?

\frac{1120\times 162}{140}=1296

Profit and loss-part-5

Problem 1: The C.P of two articles is same as RS.1200. If one article is sold at a profit of  20% and other at a loss of 25%. Find the net profit or loss?

Solution : C.P1=C.P2

Formula = \frac{P1+L1}{2}

= \frac{+20+(-25)}{2}

=\frac{-5}{2}=-2.5 (‘-‘ sign indicates loss)

Problem 2: A man sold two articles for RS.4560 each. On selling first one he gains 16\tfrac{2}{3}% and the other he loss 25%. What is the over all profit or loss percent in this transaction?

Solution: SP1=SP2=4560

P%=16\tfrac{2}{3}%=\frac{1}{6}      ,         L%=25%=\frac{1}{4}

C.P                       S.P                              P/L

6                             7                                 +1

4                             3                                  -1

We know that selling price of two articles are equal. So equal the selling price  by multiplying 3 to the first one and 7 to the second one.

C.P                       S.P                              P/L

(6                             7                                 +1 ) *3

(4                             3                                  -1 ) * 7

After multiplication

C.P                       S.P                              P/L

18                         21                               +3

28                          21                               -7

Total C.P = 18+28=46

Difference between +3 and -7 is -4

To find the profit or loss percentage = \frac{-4}{46}\times 100=\frac{-200}{23}=-8.69% Loss

‘-‘ sign indicates loss

Problem 3: By selling an article for RS.96 a person gained such that the  percentage gain equals the numerical value of C.P of the article. The C.P of an article is?

Solution: According to the problem % gain equals to the numerical value of C.P  i.e p% = C.P

We can solve this problem in a logical way

Step 1:First we have to find factors for 96

16*6=96

12*8=96

32*3=96

These are the ways that we can get 96

Step 2:Check the difference between the factors

16-6=10

12-8=4

32-3=29

Step 3:The difference between two factors should be 10

16 and 6 are such factors

Step 4:Multiply with 10

16*10=160                           6*10=60

Cost price=60 and Selling price=160

Problem 4: The cost price of an article is RS.144. A person gained such that the percentage gain equals the numerical value of S.P of the article. The selling price of an article ?

Solution : C.P=144

P%=S.P

S.P=?

Step 1:First we have to find factors for 144

16*9=144

18*8=144

These are ways that we can get 144

Step 2:Check the difference between the factors

16-9=7

18-8=10

Step 3:The difference between two factors should be 10

18 and 8 are such factors

Step 4:Multiply with 10

18*10=180                           8*10=80

Selling price =180 and cost price =80

 

Profit and loss-part-4

Problem 1: A person incurs 5% loss by selling a watch for RS 1140. At what price should the watch be sold to earn 5% profit?

Solution : Let assume C.P=100%

Loss=5%

S.P=C.P-Loss=100-5=95%

S.P=95%

To earn profit of 5%

95   \rightarrow    1140

105 \rightarrow      ?

\frac{1140\times 105}{95}=1260

Problem 2: By selling an article of RS 1050 a man losses 16\tfrac{2}{3}%. At what price he should sell the article to make a profit of 20%?

Solution : 16\tfrac{2}{3}% = \frac{1}{6}                                                20%=\frac{1}{5}

C.P               S.P           Loss                                  C.P               S.P            Profit

6                    5                  1                                      5                  6                  1

5     \rightarrow     1050

6     \rightarrow      ?(\frac{1}{5}\rightarrow1+5=6)

\frac{1050\times 6}{5}=1260

Problem 2: Profit earned by selling an article for 1060 is 20% more than the loss incur by selling an article for RS 950. At what price should the article be sold to earn 20% profit?

Solution: p%=L+20%

p  =  L+\frac{1}{5}  =  \frac{6}{5}\times L

S.P – C.P = \frac{6}{5} (C.P – S.P)

1060 – X = \frac{6}{5} (X – 950)

5300 – 5X = 6X – 5700

11X=1100

X=\frac{11000}{11}=1000

X=1000

To earn 20% profit = 1000\times \frac{120}{100}=1200

 

Profit and loss-part-3

Problem 1: C.P of 16 articles is equal to S.P of 14 articles. Find the profit or loss percentage?

Solution : C.P of 16 =S.P of 14

\frac{C.P}{S.P}=\frac{14}{16}=\frac{7}{8}

C.P=7    ,       S.P=8      Profit=1

Gain%  =   (\frac{Gain\times 100}{C.P})

=\frac{1}{7}\times 100=14\tfrac{2}{7}%

Problem 2: After selling 72 articles a man  losses S.P of 9 articles. Find the loss percent?

Solution : Let the S.P of one article = RS 1

S.P of 72 articles=72*1=72

Loss=9

C.P=72+9=81

Loss%  =   \frac{Loss\times 100}{C.P}

\frac{9}{81}\times 100=11\tfrac{1}{9}%

Problem 2: After selling 144 articles a man earns a profit of  C.P of 9 articles. Find the profit percentage?

Solution : C.P of one article = RS 1

C.P of 144 articles = RS 144

Profit = 9

Profit %   =   \frac{Profit\times 100}{C.P}

=\frac{9}{144}\times 100=6\tfrac{2}{3}%

Problem 3: After selling 10 pencils a man earns a profit of S.P of 3 pen. While selling 10 pens a man losses S.P of 4 pencils. The numerical value of profit percentage and loss percentage is equal and the C.P of pencil is half of the C.P of pen. Find the ratio of S.P of pencil and pen?

Solution : C.P of the pencil is half of the C.P of pen

Pencil                            pen

C.P                         1                 :                 2

S.P                          a                                  b

After selling 10 pencils a man earns a profit of S.P of 3 pens

C.P=10X         S.P=3b     p%=\frac{3b}{10X}\times 100

While selling 10 pens a man losses S.P of 4 pencil

C.P=2*10X=20X      S.P=4a    L%=\frac{4a}{20X}*100

The numerical value of profit percentage and loss percentage is equal

\frac{3b}{10X}\times 100   =   \frac{4a}{20X}*100

=\frac{a}{b}=\frac{3}{2}

Profit and loss-part -2

Problem 1: Find the c.p of the article which is sold at 1260 at a profit of 12.5%

Solution : covert 12.5%  into fraction

12.5%  \rightarrow \frac{1}{8}

c.p        s.p       profit

8            9             1

9   \rightarrow  1260

\rightarrow ?

\frac{1260\times 8}{9}=1120

Problem 2: A man sold an article for RS 1302 and gain profit of 16\tfrac{2}{3}%. Find the cost price of the article?

Solution :16\tfrac{2}{3}%=\frac{1}{6}

C.P             S.P           Profit

6                   7                  1

7   \rightarrow  1302

\rightarrow   ?

\frac{1302\times 6}{7}=1116

Problem 3: A shopkeeper sells an article at 14\tfrac{2}{3}%  profit on its S.P find the actual profit?

Solution : 14\tfrac{2}{3}%=\frac{1}{7}=S.P

C.P           S.P           Profit

6                 7                1

profit % (or) Gain%=  (\frac{Gain\times 100}{C.P})

\frac{1}{6}\times 100=16\tfrac{2}{3}%

Problem 4: A shopkeeper sells an article at 25% loss on its S.P. Find its actual loss?

Solution : 25% = \frac{1}{4}=S.P

C.P                S.P              Loss

5                    4                  1

Loss%   =    (\frac{Loss\times 100}{C.P})

\frac{1}{5}\times 100=20%

 

Profit and loss-part-1

It is one the topic that frequently asked in competitive exams

Here are some formulas which is used to solve the problems in profit and loss

IMPORTANT FORMULAE

  1. Gain = (S.P.) – (C.P.)
  2. Loss = (C.P.) – (S.P.)
  3. Loss or gain is always reckoned on C.P.
  4. Gain%=(\frac{Gain\times 100}{C.P})
  5. Loss%=(\frac{Loss\times100 }{C.P})
  6. Selling price=\left [ \frac{(100+GainPercent)}{100}\times C.P \right ] OR\left [ \frac{(100-LossPercent)}{100}\times C.P \right ]
  7. Cost price=\left [ \frac{100}{(100+GainPercent)}\times S.P \right ] OR \left [ \frac{100}{(100-LossPercent)}\times S.P \right ]
  8. f an article is sold at a gain of say 25%, then S.P. = 125% of C.P.
  9. If an article is sold at a loss of say, 25% then S.P. = 75% of C.P.
  10. 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{Common Loss Or Gain Percent}{10} \right )^{2}
  11. If a trader professes to sell his goods at cost price, but uses false weights, then Gain%=\left ( \frac{Error}{(True Value-Error)}\times 100 \right )%