business mathematics

Cost Price:
The price at which an article is purchased, is called its cost price,abbreviated as C.P.

Selling Price:
The price at which an article is sold, is called its selling price,abbreviated as S.P.

Profit or Gain:
If S.P. Is greater than C.P. The seller is said to have a profit or gain.

Loss:
if S.P. Is less than C.P., the seller is said to have incurred a loss.


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%=(gain*100)/C.P
5.Loss%=(loss*100)/C.P
6.S.P=[(100+gain%)/100]*C.P
7.S.P=[(100-loss%)/100]*C.P
8.C.P=(100*S.P)/(100+gain%)
9.C.P=(100*S.P)/(100-loss%)
10.If an article is sold at a gain of say,35%,then S.P=135% of C.P.
11.If an article is sold at a loss of say,35%,then S.P=65% of C.P.
12.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%=[common loss and gain %/10]2=(x/10)2
13.If a trader professes to sell his goods at cost price,but uses
false weight,then Gain%=[(error/(true value-error))*100]%
14.Net selling price=Marked price-Discount

1. The money paid by a shopkeeper to buy goods is called the cost price(C.P.) of the
shopkeeper. The price at which he sells the goods is called the selling price(S.P.) of the shopkeeper.

2. If the selling price(S.P.) is greater than the cost price(C.P.) then the shopkeeper gets profit.
Profit = Selling price - Cost price.

3.If the selling price is less than the cost price then the shopkeeper gets loss.
Loss = Cost price - Selling price.

4. For comparison of profit or loss obtained in different transactions, they are they are expressed percentages.
Suppose
S.P = Selling price, C.P = Cost price,
P = Profit, L = Loss

Ratio of profit to cost price = P : C.P.

Percentage of profit = (P/c.p)*100.

Percentage of loss = (L/c.p)*100.

PERCENTAGES - PROFIT & LOSS practice problems:

For percentage concept click: http://business-maths.blogspot.com/2008/08/percentages.html
For percentage solved problems click: http://business-maths.blogspot.com/2008/11/problems-on-percentages.html
For profit and loss concept click here
For profit and loss solved problems click here

Practice problems:

1.In a criket tournament , a team wanted its over all success rate to be 75%.After
playing half the total number of matches,it recorded only 50 % success.What per-
centage of the remaining matches should it win to achieve an overall success rate
of 75%?
a)50% b)75% c)100% d)80%


2.A man sells shoes by first quoting the selling price at a certain mark up on the
cost price.He later offers a discount on this price such that the discount
percent is the same as the mark up percent.If his cost price per pair of shoes is
Rs.300,then he makes an overall___in the transaction
a)profit b)loss c)no profit no loss d)cannot be determined

3.The respective scores of two candidates in an examination are 50% and 80% of the
maximum possible.The second candidate passes by 60 marks where as the first one
fails by 120 marks.What is the pass mark?
a)360 b)420 c)480 d)300

4.Two dining sets are sold at the same selling price resulting in a 20% gain on the
first and and 1 30% gain on the second.By what is the cost price of the fist more
than that of the second?
a)8 1/2% b)8 1/3% c)17% d)25%

5.By giving a discount of 30%,a trader makes a profit of 20%.If the trader gives a
discount of Rs 400,he would make a 20% loss.Find the marked price of the article
a)Rs 600 b)Rs 750 c)Rs 900 d)none of these

6.A bag contains balls of three different colours-Red,Blue and Green.The number of
blue balls is 12 1/2% less than the number of red balls and 40% more than the
number of green balls.By what percent is the sum of the blue and green balls less
than the sum of the red and blue balls
a)20% b)25% c)37.5% d)6 1/4%

7.The price of sugar is increased by 50%.By what percentage should the consumption
of sugar be reduced so that the expenditure on sugar is increased by 20%?
a)20% b)10% c)33 1/3% d)25%

8.A trader purchased two air conditioners.He sold both of them-one at 20% profit and
the other at 20% loss.Find the overall profit or loss percentage in the transaction
a)4% loss
b)4% profit
c)Neither profit nor loss
d)cannot be determined

9.If a profit made by selling an article at Rs.3000 is twice the loss incurred when
the article was sold at Rs.900,then find the cost price of the article
a)Rs 1800 b)Rs 1500 c)Rs 1600 d)Rs 1200

10.A trader,in an attempt to increase his sales,announces 20% discount on an article
and hence reduces his profit per article from Rs 60 to Rs 40.Find the cost price
of the article.
a)Rs 40 b)Rs 60 c)Rs 100 d)cannot be determined

11.Which of the following choices is a better bargain for a customer?
a)A single discount of 40 %
b)A discount of 25% followed by another discount of 15 %
c)Three successive disconts of 20 %,10 % and 10 % respectively
d)All the above are equally good

12.3(0.05% of 1.25) is what percent of 7.5% of 25*10^-3?
a)3% b)33 1/3% c)100 % d)1%

13.A and B start a business by investing some capital each.At the end of the year,A
receives 20% of the total profit as commission while the rest of the profit is
shared in the ratio of their respective investments.A finally receives 50% more
than what B receives.If A's capital is Rs.10,576,then B's capital is
a)Rs14,101 b)Rs 8813 c)Rs 6610 d)none of these

14.A trader,by selling 30 suitcases,gains the selling price of 5 suitcases.Find the
profit percentage per suitcase sold
a)16 2/3% b)28 4/7 % c)20% d)25%

15.A trader makes 44% profit after allowing a discount of 20% on the marked price.What is the profit percent,if a discount of 40% is allowed?
a)22% b)8% c)4.2% d)27.7%

Profit and Loss problems

Profit and Loss problems

Simple Problems

1.A man buys an article for Rs.27.50 and sells it for Rs.28.60
Find the gain percent.

Sol: C.P=Rs 27.50 S.P=Rs 28.60
then Gain=S.P-C.P=28.60-27.50=Rs 1.10
Gain%=(gain*100)/C.P%
=(1.10*100)/27.50%=4%

2.If a radio is purchased for Rs 490 and sold for Rs 465.50
Find the loss%?

Sol: C.P=Rs 490 S.P=Rs 465.50
Loss=C.P-S.P=490-465.50=Rs 24.50
Loss%=(loss*100)/C.P%
=(24.50*100)/490%=5%

3.Find S.P when C.P=Rs 56.25 and Gain=20%

Sol: S.P=[(100+gain%)/100]*C.P
S.P=[(100+20)/100]56.25=Rs 67.50

4.Find S.P when C.P=Rs 80.40,loss=5%

Sol: S.P=[(100-loss%)/100]*C.P
S.P=[(100-5)/100]*80.40=Rs 68.34

5.Find C.P when S.P=Rs 40.60,gain=16%?

Sol: C.P=(100*S.P)/(100+gain%)
C.P=(100*40.60)/(100+16)=Rs 35

6.Find C.P when S.P=Rs 51.70 ,loss=12%?

Sol: C.P=(100*S.P)/(100-loss%)
C.P=(100*51.70)/(100-12)=Rs 58.75

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

Sol: Let the new S.P be Rs x then,
(100-loss%):(1st S.P)=(100+gain%):(2nd S.P)
(100-5)/1140=(100+5)/x
x=(105*1140)/95=Rs 1260

8.If the cost price is 96% of the selling price,then what is
the profit percent?

Sol: let S.P=Rs 100 then C.P=Rs 96
profit=S.P-C.P=100-96=Rs 4
profit%=(profit*C.P)/100%
=(4*96)/100=4.17%

9.A discount dealer professes to sell his goods at cost price
but uses a weight of 960 gms for a Kg weight .Find his gain %?

Sol: Gain%=[(error*100)/(true value-error)]%
=[(40*100)/1000-40)]%=25/6%

10.A man sold two flats for Rs 675,958 each .On one he gains
16% while on the other he losses 16%.How much does he gain or
lose in the whole transaction?

Sol: loss%=[common loss or gain%/10]2=(16/10)2=2.56%

11.A man sold two cows at Rs 1995 each. On one he lost 10% and
on the other he gained 10%.what his gain or loss percent?

Sol: If loss% and gain% is equal to 10
then there is no loss or no gain.

12.The price of an article is reduced by 25% in order to
restore the must be increased by ?

Sol: [x/(100-x)]*100 =[25/(100-25)]*100
=(25/75)*100=100/3%

13.Two discounts of 40% and 20% equal to a single discount of?

Sol: {[(100-40)/100]*[(100-20)/100]}%=(60*80)/(100*100)%
=48%
single discount is equal to (100-48)%=52%

Difficult Problems

1.The cost of an article including the sales tax is Rs 616.The
rate of sales tax is 10%,if the shopkeeper has made a profit
of 12%,then the cost price of the article is?

Sol: 110% of S.P=616
S.P=(616*100)/110=Rs 560
C.P=(100*S.P)/(100+gain%)
C.P. =(100*560)/(100+12)=Rs 500

2.Sam purchased 20 dozens of toys at the rate of 375 Rs per dozen.
He sold each one of then at the rate of Rs 33.What was his
percentage profit?

Sol: C.P of one toy=Rs 375/12=Rs 31.25
S.P of one toy=Rs 33
profit=S.P-C.P=33-31.25=Rs 1.75
profit %=(profit/C.P)*100
=(1.75/31.25)*100
profit% =5.6%

3.Two third of consignment was sold at a profit of 5% and the
remainder at a loss of 2%.If the total was Rs 400,the value of the
consignment was?

Sol: let the total value be Rs x
value of 2/3=2x/3, value of 1/3=x/3
total S.P value be Rs x
total S.P=[(105% of 2x/3)+(98% of x/3)]
=(105*2x)/(100*3)+(98/100)+x/3
=308x/300
(308x/300)-x=400
8x/300=400
x=(300*400)/8=Rs 15000

4.Kunal bought a suitcase with 15% discount on the labelled price.
He sold the suitcase for Rs 2880 with 20% profit on the labelled
price .At what price did he buy the suitcase?

Sol: let the labelled price be Rs x
then 120% of x=2880
x=(2880*100)/120=Rs 2400
C.P=85% of the 2400
(85*2400)/100=Rs 2040

5.A tradesman gives 4% discount on the marked price and gives
article free for buying every 15 articles and thus gains 35%. The
marked price is above the cost price by

Sol: let the C.P of each article be Rs 100
then C.P of 16 articles=Rs (100*16)=Rs 1600
S.P of 15 articles =1600*(135/100)=Rs 2160
S.P of each article =2160/15=Rs 144
If S.P is Rs 96, marked price =Rs 100
If S.P is Rs 144,marked price =(100/96)*144=Rs 15000
therefore marked price=50% above C.P

6.By selling 33m of cloth ,one gains the selling price of 11m.Find
the gain percent?

Sol: gain=S.P of 33m-C.P of 33m
=11m of S.P
S.P of 22m=C.P of 33m
let C.P of each meter be Rs 1,then C.P of 22m=Rs 22
S.P of 22m=Rs 33
gain=S.P-C.P=33-22=Rs 11
gain%=(gain/C.P)*100
=(11/22)*100=50%


7.The price of a jewel, passing through three hands, rises on the
whole by 65%.if the first and second sellers earned 20% and 25%
profit respectively,find the percentage profit earned by the
third seller?

Sol: let the original price of the jewel be Rs P and
let the profit earned by the third seller be x%
then (100+x)% of 125% of P=165% of P
[(100+x)/100]*(125/100)*(120/100)*P=(165/100)*P
100+x=(165*100*100)/(125*120)
100+x=110
x=10%

8.When a producer allows 36% commission on the retail price of his
product ,he earns a profit of 8.8%.what would be his profit
percent if the commission is reduced by 24%

Sol: let retail price =Rs 100
commission=Rs 36
S.P=retail price-commission=100-36=Rs 64
But profit=8.8%
C.P=(100*C.P)/(gain+100)=(100*64)/(100+8.8)=Rs 1000/17
new commission=Rs 12
new S.P=100-12=Rs 88
gain=88-(1000/17)=Rs 496/17
gain%=gain*100/C.P
=(496*17*100)(17*1000)
gain%=49.6%

9.Vikas bought paper sheets for Rs 7200 and spent Rs 200 on
transport. Paying Rs 600,he had 330 boxes made,which he sold
at Rs 28 each. His profit percentage is

Sol: total investments=7200+200+600=Rs 8000
total receipt=330*28=Rs 9240
gain=S.P-C.P
=total receipt-total investments
gain=9240-8000=Rs 1240
gain% =gain*100/C.P=1240*100/8000=15.5%

10.A person earns 15% on investment but loses 10% on another
investment .If the ratio of the two investments be 3:5 ,what is the
gain or loss on the two investments taken together?

Sol: let the investments be 3x and 5x
then total investment=8x
total receipt=115% of 3x+90% of 5x
=115*3x/100+90*5x/100=7.95x
loss=C.P-S.P=8x-7.95x=0.05x
loss%=.05x*100/8x=0.625%

11.The profit earned by selling an article for Rs 900 is double the
loss incurred when the same article is sold for Rs 490 .At what
price should the article be sold to make 25% profit?

Sol: let C.P be Rs x
900-x=2(x-450)
3x=1800
x=Rs 600
C.P=Rs 600 , gain required=25%
S.P=(100+gain%)*C.P/100
S.P=(100+25)*600/100=Rs 750

12.If an article is sold at 5% gain instead of 5% loss,the seller
gets Rs 6.72 more. The C.P of the article is?

Sol: let C.P be Rs x
105% of x-95% of x=6.72
(105/100)*x-(95/100)*x=6.72
x/10=6.72
x=Rs 67.21.