## Profit and loss-part-9

Problems on marked price and discount

Important formula

discount % = $\frac{Discount}{MRP}\times&space;100$

Profit %=$M-D-\frac{M\times&space;D}{100}$

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 %=$M-D-\frac{M\times&space;D}{100}$

=$20-10-\frac{20\times&space;10}{100}$

=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 =  $\frac{200}{900}\times&space;100=\frac{200}{9}$%

p2=12.5%

p1+p2=p

$p1+p2+\frac{p1\times&space;p2}{100}$

$12.5+\frac{200}{9}+\frac{200}{9}\times&space;\frac{12.5}{100}$

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

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%  $\rightarrow$  ?

$\frac{45\times&space;100}{15}=300$

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

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    $\rightarrow$ $125\times&space;\frac{85}{100}\times&space;\frac{76}{100}$ =80.75%

100-80.75=19.25

19.25  $\rightarrow$   1078

100    $\rightarrow$    ?

$\frac{1078\times&space;100}{19.25}=5600$

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

$\frac{5}{10}\times&space;100=50$%

## 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$\rightarrow$C.P in the below equation

$\frac{7\times&space;1\times&space;5}{4}=&space;5\times&space;S.P$

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

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

1 $\rightarrow$ ?

$350\times&space;\frac{4}{7}=200$

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%

$\frac{40\times&space;100}{80}=50$

$\frac{50\times&space;120}{100}=$RS.60

RS.60  $\rightarrow$  45 Pens

RS.24  $\rightarrow$  ?

$\frac{45\times&space;24}{60}=$ 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

=$\frac{13\times&space;50\times&space;20}{100}+\frac{7\times&space;50\times&space;70}{100}$

=130+245=375

=$\frac{375}{1000}\times&space;100=37.5$

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     $\rightarrow$     ?

$\frac{240\times&space;1}{100}=2.4$

The price of banana per dozen =  $\frac{2.4\times&space;12\times&space;9}{8}=32.4$ 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=  $(\frac{Gain\times&space;100}{C.P})$

=$\frac{44\times&space;100}{100}=44$%

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%=$\frac{1}{4}$

$6\times&space;\frac{1}{4}=1.5$

6+1.5=7.5

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

$7.5\times&space;\frac{1}{5}=1.5$

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

$\frac{2}{7}\times&space;100=28\tfrac{4}{7}$%

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 $\rightarrow$RS.10

5 oranges $\rightarrow$RS.10

9 oranges $\rightarrow$RS 20

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

45*4 oranges $\rightarrow$RS.10*45

36*5 oranges $\rightarrow$RS.10*36

20*9 oranges $\rightarrow$RS 20*20

180 oranges $\rightarrow$450

180 oranges$\rightarrow$360

180 oranges$\rightarrow$400

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

360$\rightarrow$810

He sells the whole lot at 9 for RS 20

360$\rightarrow$800

810-800=10

$\frac{10}{810}\times&space;100=\frac{100}{81}=1.23$% 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%=$\frac{1}{4}$

$8\times&space;\frac{1}{4}=2$

8-2=6

The new profit becomes 20%

20%=$\frac{1}{5}$

$6\times&space;\frac{1}{5}=1.2$

6+1.2=72

9-7.2=1.8

1.8   $\rightarrow$  90

9      $\rightarrow$  ?

$\frac{90\times&space;9}{1.8}=450$

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)

$\frac{1500\times&space;2}{3}=1000$

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

= $\frac{X\times&space;16}{100}=\frac{Y\times&space;12}{100}$

=$\frac{X}{Y}=&space;\frac{3}{4}$

(3+4)7   $\rightarrow$    840

3   $\rightarrow$    ?   360

4   $\rightarrow$     ?

$\frac{840\times&space;3}{7}=360$

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

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           $S.P_{B}$=$120\times&space;\frac{35}{100}=42$

$S.P_{B}$  =120+42=162

140  $\rightarrow$   1120

162  $\rightarrow$  ?

$\frac{1120\times&space;162}{140}=1296$

## 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 = $\frac{-4}{46}\times&space;100=\frac{-200}{23}=-8.69$% 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 $\rightarrow$      ?

$\frac{1140\times&space;105}{95}=1260$

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}$$\rightarrow$1+5=6)

$\frac{1050\times&space;6}{5}=1260$

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+$\frac{1}{5}$  =  $\frac{6}{5}\times&space;L$

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 = $1000\times&space;\frac{120}{100}=1200$

## 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%  =   $(\frac{Gain\times&space;100}{C.P})$

=$\frac{1}{7}\times&space;100=14\tfrac{2}{7}$%

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%  =   $\frac{Loss\times&space;100}{C.P}$

$\frac{9}{81}\times&space;100=11\tfrac{1}{9}$%

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 %   =   $\frac{Profit\times&space;100}{C.P}$

=$\frac{9}{144}\times&space;100=6\tfrac{2}{3}$%

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%=$\frac{3b}{10X}\times&space;100$

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

$\frac{3b}{10X}\times&space;100$   =   $\frac{4a}{20X}*100$

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

## 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

$\rightarrow$ ?

$\frac{1260\times&space;8}{9}=1120$

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

$\rightarrow$   ?

$\frac{1302\times&space;6}{7}=1116$

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%=  $(\frac{Gain\times&space;100}{C.P})$

$\frac{1}{6}\times&space;100=16\tfrac{2}{3}$%

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%   =    $(\frac{Loss\times&space;100}{C.P})$

$\frac{1}{5}\times&space;100=20$%

## 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%=$(\frac{Gain\times&space;100}{C.P})$
5. Loss%=$(\frac{Loss\times100&space;}{C.P})$
6. Selling price=$\left&space;[&space;\frac{(100+GainPercent)}{100}\times&space;C.P&space;\right&space;]$ OR$\left&space;[&space;\frac{(100-LossPercent)}{100}\times&space;C.P&space;\right&space;]$
7. Cost price=$\left&space;[&space;\frac{100}{(100+GainPercent)}\times&space;S.P&space;\right&space;]$ OR $\left&space;[&space;\frac{100}{(100-LossPercent)}\times&space;S.P&space;\right&space;]$
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%=$\left&space;(&space;\frac{Common&space;Loss&space;Or&space;Gain&space;Percent}{10}&space;\right&space;)^{2}$
11. If a trader professes to sell his goods at cost price, but uses false weights, then Gain%=$\left&space;(&space;\frac{Error}{(True&space;Value-Error)}\times&space;100&space;\right&space;)$%