Profit and loss

BASICS
1) COST PRICE:
IT IS THE PRICE AT WHICH A PRODUCT IS PURCHASED. IT IS COMMONLY ABBREVIATED AS C.P.
2) SELLING PRICE:
IT IS THE PRICE AT WHICH A PRODUCT IS SOLD. IT IS COMMONLY ABBREVIATED AS S.P.
3) PROFIT OR GAIN:
IF THE SELLING PRICE OF A PRODUCT IS MORE THAN THE COST PRICE, THERE WILL BE PROFIT
IN THE DEAL.
THEREFORE, PROFIT OR GAIN = S.P. - C.P.
4) LOSS:
IF THE SELLING PRICE OF A PRODUCT IS LESS THAN THE COST PRICE, THE SELLER WILL INCUR A
LOSS.
THEREFORE, LOSS = C.P. - S.P.

5) PROFIT OR GAIN % =S.P.- C.P ∗100→PROFIT ∗100
C.P C.P
6) LOSS % = C.P.- S.P ∗100→LOSS ∗100
C.P C.P
7) IF THERE IS A PROFIT OR GAIN IN THE DEAL OR TRANSACTION;
SELLING PRICE (S.P.) = (100 + PROFIT %) ∗C.P
100
AND, THE COST PRICE (C.P.)= ( 100 )*S.P
100 + PROFIT%
8) IF THERE IS A LOSS IN THE DEAL OR TRANSACTION;
SELLING PRICE (S.P.) = (100 - LOSS %) ∗C.P
100
AND, THE COST PRICE (C.P.) = ( 100 )*S.P
100 - LOSS%

9) IF AN ARTICLE IS SOLD AT A PROFIT OF X%, THE SELLING PRICE WOULD BE EQUAL TO X% OF
COST PRICE (X/100 * C.P).
10) IF AN ARTICLE IS SOLD AT A LOSS OF X%, THE SELLING PRICE WOULD BE EQUAL TO (100-X)% OF
COST PRICE (100 - X ∗C.P).
100
11) WHEN A SELLER SELLS TWO SIMILAR ITEMS ONE AT X% GAIN AND ANOTHER ONE AT SAME (X
%) LOSS, THE SELLER ALWAYS INCURS A LOSS IN THE DEAL WHICH IS GIVEN BY:
LOSS %=(LOSS % ∗ GAIN %) %
100

METHODS TO SOLVE PROBLEMS
1) IF A SELLER CLAIMS THAT HE IS SELLING GOODS AT COST PRICE BUT USES FALSE WEIGHT TO EARN
PROFIT;
% PROFIT =(TRUE WEIGHT- FALSE WEIGHT) ∗100
FALSE WEIGHT
2) IF A SELLER SELLS A PRODUCT AT X% LOSS BUT USES WEIGHT Y INSTEAD OF Z, THE % GAIN EARNED
OR % LOSS INCURRED IS GIVEN BY:
= (100 - X)Z-100
Y
+VE SIGN WILL INDICATE PROFIT AND -VE SIGN WILL INDICATE LOSS.
3) IF A SHOPKEEPER USES WEIGHT Y GM INSTEAD OF 1 KG AND INCURS AN X% LOSS ON COST PRICE, HIS
ACTUAL GAIN OR LOSS % IS GIVEN BY:
= (100 - X)100-100
Y
+VE SIGN WILL INDICATE PROFIT AND -VE SIGN WILL SHOW THE LOSS.

4) IF A SHOPKEEPER USES WEIGHT Y GM INSTEAD OF 1 KG AND EARNS A PROFIT OF X% ON COST
PRICE, HIS ACTUAL GAIN OR LOSS % IS GIVEN BY:
= (100 + X)100-100
Y
+VE SIGN WILL INDICATE PROFIT AND -VE SIGN WILL INDICATE THE LOSS.
5) IF THERE ARE TWO SUCCESSIVE PROFITS OF X% AND Y% IN A TRANSACTION, THE RESULTANT
PROFIT IS GIVEN BY:
RESULTANT PROFIT = (X + Y +XY)
100
6) IF THERE IS A PROFIT OF X% AND LOSS OF Y% IN A TRANSACTION, THE RESULTANT PROFIT OR
LOSS IS GIVEN BY:
RESULTANT PROFIT OR LOSS = (X+Y -XY)
100

7) A SELLER SELLS A PRODUCT AT PROFIT OF X%. IF HE SELLS IT FOR RS. Z MORE, HIS PROFIT WOULD BE Y%. IN THIS CASE THE COST PRICE IS
GIVEN BY:
C.P. =
8) IF THE COST PRICE AND SELLING PRICE OF A PRODUCT ARE REDUCED BY SAME AMOUNT (X), THE COST PRICE IS GIVEN BY:
C.P. =(INITIAL PROFIT % +INCREASE IN PROFIT %) ∗ X)
INCREASE IN PROFIT %
9) IF THE COST PRICE OF P ARTICLES IS EQUAL TO THE SELLING PRICE OF Q ARTICLES, THEN PROFIT % OR LOSS % IS GIVEN BY:
10) IF A SELLS A PRODUCT TO B AT A GAIN OR LOSS OF P% AND B SELLS IT TO C AT A GAIN OR LOSS OF Q%, THE FINAL GAIN OR LOSS IS GIVEN
BY:
(P+Q+PQ)
100
11) IF A SHOPKEEPER MARKS THE PRODUCTS AT P% ABOVE THE COST PRICE AND GIVES THE CUSTOMER A DISCOUNT OF Q%, THE FINAL
PROFIT OR LOSS % IS GIVEN BY =

EXAMPLES
1. COST PRICE = RS. 60, GAIN=35% WHAT IS SELLING PRICE?
SOLUTION:
SELLING PRICE = COST PRICE + GAIN
=60 + {(35/100)*60}
=RS. 81

EXAMPLES
2. IF SURESH BUYS TWO SHEEPS AT RS. 1500 EACH AND SELLS ONE AT A GAIN OF 15% AND
ANOTHER AT A LOSS OF 15%. HOW MUCH DOES HE GAIN OR LOSS IN THE WHOLE TRANSACTION?
SOLUTION:
NEITHER LOSS NOR GAIN
EXPLANATION:
WHATEVER HE GAIN ON THE 1ST SHEEP, THE SAME HE LOSS ON THE OTHER SHEEP.

EXAMPLES
3. 20% LOSS ON SELLING PRICE IS WHAT PERCENT LOSS ON THE COST PRICE?
SOLUTION:
LET US ASSUME S.P = RS. 100, THEN LOSS = RS. 20
THEREFORE C.P = RS. 120
LOSS% = 20/120*100
=50/3
=16 2/3

EXAMPLES
4. IF THE COST PRICE IS 75% OF THE SELLING PRICE, THEN WHAT IS THE PROFIT PERCENTAGE?
SOLUTION:
ASSUME THAT THE SELLING PRICE IS RS. 100, THEN COST PRICE IS RS. 75
THEN PROFIT = RS. 25
PROFIT % =25/75*100
=100/3
=33.33%

EXAMPLES
5. A CLOTH MERCHANT MAN SAYS THAT DUE RAINY IN THE MARKET, HE SELLS THE CLOTH AT 20%
LOSS, BUT HE USES A FALSE METRE SCALE AND ACTUALLY GAIN 25%. FIND THE ACTUAL LENGTH
OF THE SCALE?
SOLUTION:
TRUE SCALE/FALSE SCALE=(100+GAIN%)/(100-LOSS%)
100/FALSE SCALE=(100+25)/(100-20)
FALSE SCALE=80*100/125
FALSE SCALE=64.

EXAMPLES
6. A CYCLE WAS PURCHASED FOR RS.1800 AND SOLD FOR RS.1300. FIND LOSS OR PROFIT?
SOLUTION:
COST PRICE = RS. 1800 ; SELLING PRICE = RS. 1500
SINCE S.P < C.P, THERE IS A LOSS
GAIN = C.P – S.P =1800 – 1500 =RS. 500 ., SO LOSS

EXAMPLES
7. A DEALER PROFESSES TO SELL HIS GOODS AT COST PRICE, BUT HE USES A WEIGHT OF 850G FOR
THE KG WEIGHT. FIND HIS GAIN PERCENT?
SOLUTION:
% PROFIT =(TRUE WEIGHT- FALSE WEIGHT) ∗100
FALSE WEIGHT
ERROR =TRUE WEIGHT-FALSE WEIGHT
=1KG – 850G
=1000G – 850 G =150G
PROFIT %=(150/850)*100
= 17 11/17
THEREFORE, GAIN%= 17 11/17

EXAMPLES
8. A MAN BOUGHT A BUFFELOW AND A CARRIAGE FOR RS.3000, HE SOLD THE BUFFELOW AT A GAIN OF 20% AND THE
CARRIAGE AT A LOSS 10% THEREBY GAINING 2% ON THE WHOLE. FIND THE COST OF BUFFELOW?
SOLUTION:
LET THE COST OF BUFFELOW IS X RUPEES.
THEN THE COST PRICE OF CARRIAGE = RS. (3000 – X)
(20% OF X) – (10% OF (3000 – X) = 2% OF 3000
{(20/100)*X} – {(10/100)(3000 – X)} = {(2/100)*3000}
{X/5} – {(3000 – X)/10)} = 3000/50
MULTIPLY BY 10 ON BOTH SIDES, THEN
2X – 3000 + X = 600
3X = 3600
X=1200
THEREFORE, THE COST OF BUFFELOW IS RS.1200

EXAMPLES
9. A MAN BUY A CYCLE FOR RS. 1600 AND SELLS IT AT A LOSS 20%. WHAT IS SELLING PRICE?
SOLUTION:
C.P = RS. 1600, LOSS=20% ; S.P = ?
SELLING PRICE = COST PRICE - (20% OF 1600)
=1600 - {(20/100)*1600}
=1600 – 320
=1280
SELLING PRICE = RS. 1280

PRACTICE QUESTIONS
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