## Profit and Loss Part 1

It is one of the topics that frequently asked in competitive exams

Here are some formulas which are 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%=$\left&space;(&space;\frac{Error}{(True&space;Value-Error)}\times&space;100&space;\right&space;)$%

## 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 a 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 3

Problem 1: Cost Price (C.P) of 16 articles is equal to Selling Price (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 3: 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 4: After selling 10 pencils a man earns a profit of S.P of 3 pens. 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 the pencil is half of the C.P of the pen. Find the ratio of S.P of pencil and pen?

Solution: C.P of the pencil is half of the C.P of the 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 4

Problem 1: A person incurs a 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 3: Profit earned by selling an article for 1060 is 20% more than the loss incurs 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 5

Problem 1: The C.P of two articles is the 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 the first one he gains $16\tfrac{2}{3}$% and the other he lost 25%. What is the overall 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 the selling price of the two articles is 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

‘-‘ 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 the 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 the 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