Important Facts:
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.
Formula
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
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%
