PROFIT AND LOSS ARTHMETIC MATERIAL

PROFIT AND LOSS

.....................

IF SP > CP

PROFIT = SP-CP

IF CP > SP

LOSS = CP - SP

PROFIT % = (PROFIT/CP)*100

LOSS % = (LOSS/CP )* 100

EG:

A MAN BOUGHT A BOOK FOR 200 RS AND SELLS IT FOR 240 RS WHAT IS HIS GAIN PERCENTAGE?

GAIN = 240-200

PROFIT % = (40/200)*100

20%

EG:

A SHOPKEEPER PURCHASED A BOX FOR RS 300 AT WHAT PRICE HE HAS TO SELL TO GET A GAIN OF 15%?

15% = (P/300)*100

P = (15/100)*300

PROFIT +CP = 300+45

345

METHOD 2

PROFIT 15%

100%.....................300

115%....................?

345

EG:

BY SELLING A HAT FOR 500 RS A PROFIT OF 25% IS MADE FIND THE COST PRICE OF THE HAT?

PROFIT 25%

SO 125% ......... 500

100% .........?

400

EG:

IMPORTANT TABLE

PROFIT % COST PRICE PROFIT/LOSS SELLING PRICE

20% 100 25 125

15% 100 15 115

35% 100 35 135

-10% 100 -10 90

-45% 100 -45 55

EG:

BY SELLING AN ARTICLE FOR RS 640 A LOSS OF 20% IS MADE FIND THE COST PRICE OF THE ARTICLE ?

80% ..........640

100%...........?

(100*640)/80

800

EG:

BY SELLING A BOOK FOR 540 RS A GAIN OF 20% IS MADE IF IT IS SOLD TO LOSS OF 20% WHAT WILL BE

THE SELLING PRICE?

120 % --------540

80%...........?

(80*540)/120

360

EG:

A GAIN OF 30% IS MADE BY SELLING A BOOK FOR RS 520 RS AT WHAT PRICE IT SOLD TO GAT A GAIN OF 60%?

130%---------520

160%...........?

(160*520)/130

640

EG:

BY SELLING A WATCH FOR 480 RS A PROFIT OF 20% IS MADE WHAT IS THE GAIN OR LOSS PERCENTAGE

IF IT IS SOLD FOR RS 380?

120%--------480

? ........380

(120*380)/480

95%

100-95

5% LOSS

EG:

MR RAMU SOLD A PEN AT 12% PROFIT HAD HE SOLD IT FOR 24RS MORE HE WOULD HAVE GAINED 18%

WHAT IS THE COST PRICE OF PEN?

18-12 = 6%

6% ...........24

100% ---?

400

RAJESH SOLA AN ARTICLE AT 10% LOSS IF HE HAD TAKEN 98 RS MORE HE WOULD HAVE GAINED 4% WHAT

IS THE COST PRICE OF THE ARTICLE?

10-(-4)

14%..........98

100%...............?

(100*98)/14

700

EG:

SURYA PURCHASES 2 BOOKS AT 300 RS HE SOLD ONE BOOK AT 10% GAIN AND OTHER BOOK AT 10% LOSS

WHAT IS THE TOTAL LOSS OR GAIN PERCENTAGE?

CP 100 .....300

110....?

330

CP 100.......300

90.......?

270

CP1 +CP2 = 330+270 = 600

300+300 = 600

BOTH SAME SO NO PROFIT AND NO LOSS

EG:

A COMPANY SELLS TWO CELLPHONES AT 24000 EACH ON ONE HE GAINED 20% AND OTHER LOSS 20%

WHAT IS THE OVERALL GAIN OR LOSS PERCENTAGE?

CP1 :

120 ------- 24000

100 ..........?

20000

CP2 :

80 ...........24000

100...........?

30000

CP1+CP2 = 20000+30000

50000

SP1+SP2 = 24000+24000

48000

50000

48000

..............

2000

(2000/50000)/100

4% LOSS

IF THE COST PRICE OF THE TWO ARTICLES ARE EQUAL AND A LOSS OF X PERCENT ON 1 IS EQUAL TO A

GAIN OF X PERCENT ON OTHERTHAN OVERALL TRANSACTION THERE WILL BE NO LOSS OR NO PROFIT

IF SELLING PRICE OF TWO ARTICLES ARE SAME AND A GAIN OF X PERCENTAGE ON ONE ARTICLE IS EQUAL TO ALOSS OF X% ON THE OTHER THEN

IN OVERALL TRANSACTION THEIR WILL BE ALWAYS LOSS OF (X*X)/100%

EG:

A SHOPKEEPER SELLS TWO BOOKS FOR 520 RS EACH ONE HE GAINS 30% ON THE FIRST AND LOSES 20%

ON THE OTHER WHAT IS THE GAIN OR LOSS PERCENTAGE IN THE OVERALL TRANSACTION?

CP1 130 -------520

100 ........?

400

80-------520

CP2

100..........?

650

SP = 520+520

1040

SP = 650+400

1050

(10/1050)*100

EG:

IF THE RATIO OF COST PRICE AND SELLING PRICE IS 5 : 6

FIND THE GAIN PERCENTAGE?

5 -------100

..................

6 .......120

20%

PROFIT % = (P/CP)*100

(1/5)*100

20%

EG:

A MAN BUYS AN ARTICLE FOR 10% LESSTHAN ITS VALUE AND SELLS IT FOR RS 10% MORE THAN ITS VALUE HIS GAIN OR LOSS PERCENTAGE IS

A) LESS THAN 20%

B) MORE THAN 20%

C) 20% PROFIT

D) CAN NOT BE DETERMAINED

90 .......100........110

CP SP

(20/90)*100

22(2/9)%

ANS B

EG:

BY SELLING AN ARTICLE PER RS 960 A PROFIT OF 20% IS MADE FIND THE COSTPRICE OF THE ARTICLE?

960.......120

?.........100

(960*100)/(120)

800

IF THE COST PRICE OF 20 ARTICLES IS EQUALS TO SELLING PRICE OF 16 ARTICLES WHAT IS THEW GAIN OR LOSS %?

CP(20) = SP(16)

CP 20 = SP 16

CP/SP = 16/20

4/5

P% = (1/4)*100

25%

EG:

THE COST PRICE OF 10 TABLES IS EQUALS IS EQUALS TO SELLING PRICE OF 20 TABLES WHAT IS THE LOSS PERCENTAGE?

CP(10) = SP(20)

CP/SP = 1/2

LOSS PERCENTAGE = (1/2)*100

50%

EG:

BY SELLING 33 METERS OF CLOTH THE MAN GAINS THE SELLING PRICE OF 11 METERS OF CLOTH FIND HIS GAIN

OR LOSS PERCENTAGE?

SP = CP +PROFIT

SP(1) = CP(1) +PROFIT(1)

SP(33) = CP(33) +PROFIT(33)

SP(22) = CP(33)

SP/CP = 33/22

PROFIT PERCENTAGE

(11/22)*100

50%

EG :

BY SELLING 33 APPLES A MAN GAINS COSTPRICE OF 11 APPLES FIND HIS GAIN PERCENTAGE?

SP = CP+PROFIT

SP(33) = CP(33) +CP(11)

SP/CP = 44/33

4/3

(1/3)*100

33(1/3)%

EG:

IF PENCILS ARE PURCHASED AT 5 PER A RUPEE HOW MANY MUST BE SOLD FOR RS 1 TO GET PROFIT OF 25%?

1......5 CP/SP = 1/5 = 20P

P% = 25%

CP ......100% .......20P 1/5

125%.........? 1/4 100/25 = 4

EG :

A SHOPKEEPER BUYS PENS AT 9 PER 10 RS AND SELLS THEM AT 10 PER RS 9 WHAT IS HIS LOSS OR GAIN PERCENTAGE?

9 PENS 10

90 PENS 100

10 PENS 9

90 PENS 81

100 TO 81 DECREASED -19%

EG:

A PERSON BUYS AN ITEM 5 PER 4 RS AND SELLS 4 PER 5 GAIN PERCENTAGE?

20 ........16

20...........25

9% PROFIT

PROFIT PERCENTAGE (9/16)*100

56(1/4)%

EG:

A MAN BUYS EGGS AT 2PER 1 RS AND AN EQUAL NUMBER AT 3 PER RS 2 ANBD SELLS THE WHOLE AT 5 PER 3 RE FIND

HIS GAIN OR LOSS PERCENTAGE?

COSTING

2 EGGS 1

3 EGGS 2

SELLING

5 EGGS 3

LCM 30 (2,3,5)

30 ...15 5......3

*12 *12

30 ...20 60.....36

.........................

60 35

P% = (1/35)*100

EG:

THE LOSS OBTAINED BY SELLING AN ARTICLE PER 70

SAME AS THE GAIN OBTAINED BY SELLING IT FOR 120 RS

SP = 70

SP = 120

CP-X = 70

CP+X = 120

2CP = 190

CP = 95

EG:

DAVID SELLS A BICYCLE TO RAJU AT 40% PROFIT RAJU SELLS IT TO MOHAN AT 10% LOSS IF MOHAN

PAYS 2520 PER HIM AT WHAT PRICE DID DAVID BUY IT?

40% -10%

100 DAVID............> RAJU..................> MOHAN

*20

........... 140 140-14 = 126

2000 * 20

.............

2520

EG:

A DISHONEST DEALER PROMISES TO SELL SUGAR AT THE COST PRICE BUT USES A WEIGHT OF 900 GRMS INSTEAD OF 1KG WHAT IS HIS GAIN PERCENTAGE?

10000

CP PROFIT

900 100

1000-900

100

(PROFIT/CP)*100

( 100/900)*100

11(1/9)%

FOR CUSTOMER IT IS A LOSS OF 10%

EG:

IF GOODS ARE PURCHASED FOR 6000 RS 1/4 TH IS SOLD AT A LOSS OF 20% AND THE REMAINING WERE

SOLA AT 10% PROFIT WHAT IS THE OVERALL GAIN OR LOSS PERCENTAGE?

TOTAL 6000

1/4 3/4

-20% +10%

1500 4500

-300 450

......................

1200 4950

6150

6150-600

150

(150/6000)*100

2.5%

EG:

A SHOPKEEPER MARKS HIS GOODS 20% ABOVE THE COST PRICE BUT ALLOWS A DISCOUNT OF 10% WHAT IS HISS

GIAN OR LOSS PERCENT?

MP 10% DISC

100......>120......>108

MARKED PRICE 120

DISCOUNT 120-12

108

EG:

A CLOTH MERCHANT ALLOWS TWO SUCCESSIVE DISCOUNTS OF 20% and 20%

find his discount after two successive changes?

100..........>80.................>64

20 -16

successive changes

if x% and y % are two successive changes on a single article then overall change is given by

x+y+(xy)/100

-20-20+(20*20)/100

-40+4

-36%

discount % = (discount/market price )*100

EG:

AFTER DELETING COMISSION OF 5% A TV SET COST 9595 FIND ITS MRP?

9595.......95%

?..........100%

(9595*110)/(95)

10100

EG:

A SHOP KEEPER SELLS A TV ON DISCOUNT 8% ON PRINTED PRICE AND GAINS 25% IF PRINTED PRICE

WAS 20000 RS THEN FIND ITS COST PRICE?

PRINTED PRICE 20000

DISCOUNT 8% =1600

.......................

18400

18400...........125

?.................100

14720

EG:

A SHOPKEEPER MARKS HIS GOODS 20% ABOVE THE COST PRICE AND ALLOWS THE PURCHASE FOR A DISCOUNT

OF 10% FOR CASH PAYMENT FIND PROFIT?

MP TO SP ...........> DISCOUNT

CP TO MP.............> PROFIT

+20 -10

CP.........> MP..........>SP

100 120 108

8% PROFIT

EG:

A SHOPKEEPER OFFERS 10% DISCOUNT ON AN ARTICLE AND STILL MAKES A PROFIT OF 20% TO HIM

WHAT IS THE ANNUAL COST OF THE ARTICLE MARKED 500 RS?

10% DISCOUNT ON 500 450

PROFIT 20%

120% ...........450

100% .........?

375

EG:

A SHOPKEEPER SOLD AN ARTICLE OFFERING A DISCOUNT OF 5% AND EARNED A PROFIT OF 23.5%

WHAT WOULD HAVE BEEN THE PERCENTAGE OF PROTIF EARNED IF THE NO DISCOUNT HAS BEEN OFFERED?

-10%

CP ............> MP ...........>SP

23.5%

NO DISCOUNT ALLOWED MEANS WE HAVE TO FIND THE PERCENTAGE OF MARK PRICE ABOVE THE COST PRICE

CP...........SP........MP

95%MP

125%CP

95%MP.............123.5%CP

100%MP.............?

(100*123.5)/95

130%

EG:

A SHOPKEEPER OBTAINS A PROFIT OF 20% AFTER ALLOWING A DISCOUNT OF 10% ON MARKED PRICE HOW

MUCH PERCENTAGE ABOVE THE COST PRICE IS THE MARKED PRICE?

20% 10%

CP<........SP<.........100

100%CP 90%

120%CP = 90%OF MP

?CP = 100%OF MP

(120*100)/90

133(1/3)

METHOD 2

X - 10-(10X/100) = 20

9X/10 = 30

X = 300/9

100/3

EG:

A SHOPKEEPER EARNS A PROFIT OF 15% AFTER SELLING A BOOK AT 20% DISCOUNT ON THE PRINTED PRICE THE RATIO

OF THE COST PRICE AND PRINTED PRICE OF THE BOOK?

20%

CP ..........SP..........MP

115%CP

80%MP

CP/MP = 80/115

16/23

EG:

THE MARKED PRICE OF A ARTICLES IN A SHOP ARE 20%MORE THAN COST PRICE THE SHOPKEEPER GIVES A DISCOUNT OF 40 RS ON PURCHASE OF 960

WHAT IS THE NET PROFIT %?

CP........MP........SP

800 +20% 960 -40 920

920-800 = 120

EG:

THE DIFFERENCE BETWEEN A DISCOUNT OF 35% AND TWO SUCCESSIVE DISCOUNT OF 20% AND 205 ON A CERTAIN BILL

WAS 22 RS FIND AMOUNT OF BILL?

-20-20+(400/100)

-36

DIFF 35 TO 36 = 1%

1% .....22

100%.....?

2200

EG:

THE DIFFERENCE BETWEEN SUCCESSIVE DISCOUNTS OF 40% FOLLOWD BY 30% AND 45% FOLLOWED BY 20% ON THE

MARKED PRICE OF A SHIRT IS 12 RS WHAT IS THE MARKED PRICE OF THE SHIRT?

-40-30+12 = -58

-45-20+9 = -56

2%..........12

100%...........?

(100*12)/2

600

EG:

FIND A SINGLE DISCOUNT IS EQUALS TO SERIED DISCOUNTS OF 10% 20% AND 40%?

-10 -20 -40

-10 -20+2

-28 -40+ 11.2

-68+11.2

-56.8

METHOD 2

100................90.........72.........56.8

-20 -40

EG :

A MAN BAUGHT A BOOK FOR 500 RS AND SOLD IT FOR 20% PROFIT FIND SELLING PRICE?

SP = CP + PROFIT

500 + (20% OF 500)

600

EG:

A MAN BAUGHT AN ITEM FOR 600 RS AND SOLD IT FOR 10% LOSS THEN FIND SELLING PRICE?

10% OF LOSS IN 600

(10/100)*600

600-60

540

EG:

BY SELLING AN ITEM FOR 600 RS A PROFIT OF 20 % MADE FIND COST PRICE?

COST PRICE = 100%

SELLING PRICE = 100% +20%

120%

120% -------600

1%..........?

(600/120)

500

PROFIT = 600-500

EG:

BY SELLING AN ITEM FOR 360 RS A LOSS OF 10% MADE FIND LOSS?

10 % LOSS

SO 90% SP - 360

1 % ..?

4RS

100%......400RS

LOSS : 400 - 360

EG:

A MAN SOLD AN ITEM FOR 5 % PROFIT HAD HE SOLD IT FOR 24RS MORE HE WOULD HAVE GAINED 8 % PROFIT FIND

COST PRICE?

DIFFERENCE 8%-5% = 3%

3%...........24 RS

1%............8

100%.....800RS

EG:

A MAN SOLD AN ITEM FOR 5% LOSS HAD HE SOLD IT FOR 30RS MORE HE WOULD HAVE GAINED 10% PROFIT

FIND COST PRICE?

DIFFENECE (10%- (_5%)

15%''

15%-----30RS

1%......2RS

100%......200RS

EG:

A MAN SOLD AN ITEM FOR 5% LOSS HAD HE SOLD IT FOR 40RS MORE HE WOULD HAVE GAINED 5% PROFIT FIND COSTPRICE?

-5 TO 5 % = 10%

10% --- 40

1%......?

100%........400RS

EG:

IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3 : 2

THE FIND BOYS PERCENTAGE (3/5)*100

60%

FIND GIRLS PERCENTAGE (2/5)*100 = 40%

BOYS ARE HOW MUCH PERCENTAGE MORE THAN GIRLS

(NUMBER OF BOYS - NUMBER OF GIRLS)/NUMBER OF GIRLS *100

(3-2)/2

(1/2)*100

50%

GIRLS ARE HOW MUCH PERCENTAGE MORE THAN BOYS?

(NUMBER OF GIRLS - NUMBER OF BOYS)/NUMBER OF BOYS

(1/3)*100

33(1/3)%

COMPARE BOYS WITH GIRLS THEN FIND PERCENTAGE

(3/2)*100

150%

COMPARE GIRLS WITH BOYS THEN FIND PERCENTAGE ?

(2/3)* 100

200/3

66(2/3)%

EG:

A MAN WEIGHT INCREASED FROM 60 KGS TO 72 KGS THEN FIND PERCENTAGE OF INCREASE IN WEIGHT?

72-60

INCREASE ALWAYS COMPARE WITH INITIAL

INITIAL = 60

(12/60)*100

20%

EG:

A MAN WEIGHT DECREASE FROM 60 TO 51 KGS THEN FIND DECREASE PERCENTAGE?

60 - 51

INITIAL 60

(9/60)*100

15%

EG:

A SALARY IS 20% LESS THAN B SALARY THEN FIND B SALARY IS HOW MUCH MORE THAN A SALARY?

A B

80 100

(20/80)*100

25%

EG:

SHORT CUT FORMULAE :

(X/(X+100))*100% INCREASE

(X/(X-100))*100% DECREASE

(20/(100-20))*100%

(20/80)*100

25%

EG:

ONE VALUE FIRST INCREASED TO 25% THEN HOW MUCH MUCH IT WILL BE REDUCED TO GET THE INITIAL VALUE?

(25/125)*100

20%

EG:

A RECTANGLE LENGTH INCREASED BY 20% HOW MUCH ITS BREADTH WILL BE DECREASED TO

NO CHANG IN AREA?

(20/120)*100%

16(2/3)%

EG:

PROFIT PERCENTAGE : (DIFFERNECE)/(LOWEST VALUE) *100%

LOSS PERCENTAGE = (DIFFERENCE)/(HIGHEST VALUE)*100%

EG:

ONE ITEM BOUGHT FOR 500 RS AND SOLD IT FOR 60 RS THEN FIND PROFIT PERCENTAGE?

(100/500)*100%

20%

EG:

ONE ITEM BAUGHT FOR 500 RA AND SOLD IT FOR 425 RS THEN FIND LOSS PERCENTAGE?

(75/500)*100%

15%

Allegation

EG:

IN A CLASS AVERAGE AGE OF 60 STUDENTS IS 15 YEARS AVERAGE AGE OF BOYS IS 13 YEARS AND GIRLS IS 16

YEARS FIND NO OF BOYS AND NO OF GIRLS?

BOYS GIRLS

13 16

16-15= 1 15-13 = 2

3 PARTS 60

1 PART ?

60/3 = 20

2*20 = 40

20,40

EG:

IN A SOLUTION THERE IS 20% FINISHED

IN ANOTHER THERE IS 30% FINISHED

HOW MANY LITERS OF FIRST SOLUTION IS MIXED WITH 60 LITERS OF SECOND SOLUTION SO THAT THERE IS

24% IN THE MIXURE?

1 2

20 30

30-24 = 6 24-20 = 4

6 4

SO 3 :2

2 PARTS 60

3 PARTS 90

EG:

A MAN BOUGHT 2 ARTICLES FOR RS 600 ONE ARTICLE IS SOLD AT 10% PROFIT AND ANOTHER ARTICLE

SOLD AT 5% LOSS OVERALL THERE IS NO LOSS OR NO GAIN FIND THE COST OF EACH ARTICLE ?

SAY PERCENTAGE 100%

1 2

110 95

100

5 10

1 2

3 ----------600

1 .........?

200,400

EG:

A MAN BORROWED RS 60,000 IN 2PARTS ONE AT 3% AND ANOTHER AT 6% RATE OF INTERESTIF TOTAL

SIMPLE INTEREST FOR 1 YEAR IS RS 3000 FIND THE MONEY LENDED 2% PER ANUM?

100%........60,000

1%..........?

600

1 2

3% 6%

3000

600 1200

1 2

3.....60000

1 ......?

60000/3 = 20000

EG:

POPULATION OF A TOWN IS 10000 IF MALES INCREASED BY 3% AND FEMALE INCREASED BY 8% THEN THE

OVERALL POPULATION BECOMES 10,500 FIND NO OF FEMALES?

1% .........100

300 800

500

300 200

3 2

5............10000

3........?

6000

4000

EG:IN A BAG THERE ARE 80 COINS PARTIY OF 50 PAISE AND PARTLY OF 25 PAISE THE TOTAL AMOUNT

IN THE BAG 36 RA FIND THE TOTAL NO OF 50 PAISEAND NO OF 25 PAISE COINS?

50P 20P

40 20

16 4

4 1

5 .............80

4............?

(4*80)/5

EG:

IN AN EXAM THERE ARE 40 QUESTIONS A STUDENT GET 3 MARKS FOR EVERY CORRECT ANSWER

1 CMARK DEDUCTION FOR EVERY WRONG ANSWER A STUDENT ATTENDED ALL THE QUESTIONS AND GOT 88 MARKS

CORRECT ANS ? WRONG ANS?

120 - 40

128 32

4 1

5..........40

1......?

40/5 = 8

WRONG 8 CORRECT 32

METHOD 2

3C-1W = 88

C+W = 40

..................

4C = 128

C = 32

W = 8

EG:

IN A GARDEN THERE ARE SOME PIGEONS AND RABBITS TOTAL NUMBER OF HEADS 60 TOTAL NO OF LEGS 150 FIND

THE NO OF PIGEONS AND RABBITS?

P R

120L 240

150

90 30

3 1

4.........60

3......?

(3*60)/4

EG:

COST OF 1 VARIETYRICE IS 16 PER KG

AND ANOTHER RICE IS RS 20 PER KG

FIND IN WHICH RATIO THERE ARE MIXED SO THAT BY SELLING THE MIXURE AT RUPEES 19.80 PER KG

THERE IS A PROFIT OF 10%?

1 16

2 20

1,2 @10% OF PROFIT = 19.80

16 10% = 16.0

1.6

.......

17.6

20 10% = 20.0

2.0

..........

17.60 22

19.80

2.20 2.20

1 1

EG:

COST OF 1 LETER PURE MILK IS RS 30 AFTER MIXING WATER IN THAT DILUTED MILK IS SOLDED

AT RS 30 THERE MILK AND WATER ARE MIXED?

M = 30 @25% = 37.5

W = 0 = 0

M+W = 25%

PROFIT 30

M W

37.5 0

30 7.5

2 3

EG:

IN A CLASS 60 STUDENS AVERAGE AGE IS 15 YEARS

BIYS AGERAGE IS 16 YEARS GIRLS AVERAGE AGE IS 13 YEARS THEN FIND HOW MANY BOYS AND HOW MANY GIRLS?

B G

16 13

2 1

TOTAL 60

3 PARTS 60

1 PART ?

1 PART 20

EG:

IN A CLASS BOYS AVERAGE WEIGHT 40 KGS GIRLS AVERAGE WEIGHT 30 KGS

TOTAL STUDENTS AVERAGE WEIGHT 34 KGS IN THAT CLASS IF THERE ARE 12 BOYS FIND HOW MANY GIRLS?

40 30

2 3

2P = 12

P =6

3*6 = 18

EG:

WE HAVE TO DISTRIBUTE 2.50 RS TO 100 STUDENTS IN AN AVERAGE BOYS CAN CAN 3.10 PAISE

GALS CAN GET 2.10 PAISE THEN FIND BOYS AND GIRLS?

100 STUDENTS AVG = 2.50

1 STUDENT AVERAGE = 2.50 RS

BOYS AVG = 3.10

GIRLS AVERAGE = 2.10

3.10 2.10

2.50

.40 .60

50 60

2 3

40 BOYS 60 GIRLS

EG:

IN A SOLUTION 20 % MILK IN B SOLUTION 30% MILK 14 LETERS FIRST SOLUTION IS WITH

X LITERS OF B SOLUTION THEN NEW SOLUTION FORMED IN THAT SOLUTION 28% MILK

FIND X?

1 2

20% 30%

28%

2 8

1 4

1 PART 14 L

4 PARTS 56

EG:

ANAND BAUGHT 2 ITEMS WITH 500 RE ON FIRST ITEM 10% ON SECOND ONE 20% THEN HE GOT OVERALL PFROFIT

OF 14% ON THOSE TWO ITEMS FIND WITHHOW MUCH COST HE BAUGHT THOSE TWO ITEMS?

1 2

10 20

6 4

RS 50O 3 2

300 200

EG:

PRAMOD BAUGHT 2 ITEMS FOR RS 500 RE HE SOLD FIRST ITEM FOR 10% PROFIT AND 2 ND ITEM FOR 5% LOSS THEN

OVERALL NO LOSS AND NO GAIN ON TWO ITEMS THEN FIND WITH HOW MUCH COST HE HE BOUGHT THOSE TWO ITEMS?

10% PROFIT 5% LOSS

110% 95%

100%

5% 10%

1 2

3 PARTS = 600

1 PART = 200

EG:

SIDDHU DIVIDED 600RS INTO TWO PARTS FIRST PART HE LENDED AT THE RATE OF 3%

2ND PART LENDED AT THE RATE OF 6% THEN HE GOT TOTAL INTEREST 300 RS

FIND THE AMOUNT LENDED FOR 3%?

600RS

1% = 60

3% 180

6% 360

1 2

180 360

300

60 120

1 2

1 PART 2000

3 PART 6000

EG:

IN A TOWN 35000 POPULATIUON 6% MALE AND 4 % FEMALE INCREASED THEN TOTAL POPULATION INCREAED TO 36766 THEN FIND

HOW MANY MALE AND HOW MANY FEMALE?

MALE FEMALE

6% 4%

2100 1400

1760

360 340

18 17

35000 = 35PARTS

1 PART = 1000

18000 17000

IN A GARDEN SOME HENS AND SOME GOATS

TOTAL HEADCOUNT IS 60 AND TOTAL LEGS IS 150 THEN FIND TOTAL HENS AND TOTAL GOATS?

HEADS LEGS

ASSUM TOTAL HENS 120 240 TOTAL GOATS

120 240

150

90 30

3 1

4 PARTS 60

1 PART 15

GOAT 15 HENS 45

Allegation

EG:

IN A CLASS AVERAGE AGE OF 60 STUDENTS IS 15 YEARS AVERAGE AGE OF BOYS IS 13 YEARS AND GIRLS IS 16

YEARS FIND NO OF BOYS AND NO OF GIRLS?

BOYS GIRLS

13 16

16-15= 1 15-13 = 2

3 PARTS 60

1 PART ?

60/3 = 20

2*20 = 40

20,40

EG:

IN A SOLUTION THERE IS 20% FINISHED

IN ANOTHER THERE IS 30% FINISHED

HOW MANY LITERS OF FIRST SOLUTION IS MIXED WITH 60 LITERS OF SECOND SOLUTION SO THAT THERE IS

24% IN THE MIXURE?

1 2

20 30

30-24 = 6 24-20 = 4

6 4

SO 3 :2

2 PARTS 60

3 PARTS 90

EG:

A MAN BOUGHT 2 ARTICLES FOR RS 600 ONE ARTICLE IS SOLD AT 10% PROFIT AND ANOTHER ARTICLE

SOLD AT 5% LOSS OVERALL THERE IS NO LOSS OR NO GAIN FIND THE COST OF EACH ARTICLE ?

SAY PERCENTAGE 100%

1 2

110 95

100

5 10

1 2

3 ----------600

1 .........?

200,400

EG:

A MAN BORROWED RS 60,000 IN 2PARTS ONE AT 3% AND ANOTHER AT 6% RATE OF INTERESTIF TOTAL

SIMPLE INTEREST FOR 1 YEAR IS RS 3000 FIND THE MONEY LENDED 2% PER ANUM?

100%........60,000

1%..........?

600

1 2

3% 6%

3000

600 1200

1 2

3.....60000

1 ......?

60000/3 = 20000

EG:

POPULATION OF A TOWN IS 10000 IF MALES INCREASED BY 3% AND FEMALE INCREASED BY 8% THEN THE

OVERALL POPULATION BECOMES 10,500 FIND NO OF FEMALES?

1% .........100

300 800

500

300 200

3 2

5............10000

3........?

6000

4000

EG:IN A BAG THERE ARE 80 COINS PARTIY OF 50 PAISE AND PARTLY OF 25 PAISE THE TOTAL AMOUNT

IN THE BAG 36 RA FIND THE TOTAL NO OF 50 PAISEAND NO OF 25 PAISE COINS?

50P 20P

40 20

16 4

4 1

5 .............80

4............?

(4*80)/5

EG:

IN AN EXAM THERE ARE 40 QUESTIONS A STUDENT GET 3 MARKS FOR EVERY CORRECT ANSWER

1 CMARK DEDUCTION FOR EVERY WRONG ANSWER A STUDENT ATTENDED ALL THE QUESTIONS AND GOT 88 MARKS

CORRECT ANS ? WRONG ANS?

120 - 40

128 32

4 1

5..........40

1......?

40/5 = 8

WRONG 8 CORRECT 32

METHOD 2

3C-1W = 88

C+W = 40

..................

4C = 128

C = 32

W = 8

EG:

IN A GARDEN THERE ARE SOME PIGEONS AND RABBITS TOTAL NUMBER OF HEADS 60 TOTAL NO OF LEGS 150 FIND

THE NO OF PIGEONS AND RABBITS?

P R

120L 240

150

90 30

3 1

4.........60

3......?

(3*60)/4

EG:

COST OF 1 VARIETYRICE IS 16 PER KG

AND ANOTHER RICE IS RS 20 PER KG

FIND IN WHICH RATIO THERE ARE MIXED SO THAT BY SELLING THE MIXURE AT RUPEES 19.80 PER KG

THERE IS A PROFIT OF 10%?

1 16

2 20

1,2 @10% OF PROFIT = 19.80

16 10% = 16.0

1.6

.......

17.6

20 10% = 20.0

2.0

..........

17.60 22

19.80

2.20 2.20

1 1

EG:

COST OF 1 LETER PURE MILK IS RS 30 AFTER MIXING WATER IN THAT DILUTED MILK IS SOLDED

AT RS 30 THERE MILK AND WATER ARE MIXED?

M = 30 @25% = 37.5

W = 0 = 0

M+W = 25%

PROFIT 30

M W

37.5 0

30 7.5

2 3

EG:

IN A CLASS 60 STUDENS AVERAGE AGE IS 15 YEARS

BIYS AGERAGE IS 16 YEARS GIRLS AVERAGE AGE IS 13 YEARS THEN FIND HOW MANY BOYS AND HOW MANY GIRLS?

B G

16 13

2 1

TOTAL 60

3 PARTS 60

1 PART ?

1 PART 20

EG:

IN A CLASS BOYS AVERAGE WEIGHT 40 KGS GIRLS AVERAGE WEIGHT 30 KGS

TOTAL STUDENTS AVERAGE WEIGHT 34 KGS IN THAT CLASS IF THERE ARE 12 BOYS FIND HOW MANY GIRLS?

40 30

2 3

2P = 12

P =6

3*6 = 18

EG:

WE HAVE TO DISTRIBUTE 2.50 RS TO 100 STUDENTS IN AN AVERAGE BOYS CAN CAN 3.10 PAISE

GALS CAN GET 2.10 PAISE THEN FIND BOYS AND GIRLS?

100 STUDENTS AVG = 2.50

1 STUDENT AVERAGE = 2.50 RS

BOYS AVG = 3.10

GIRLS AVERAGE = 2.10

3.10 2.10

2.50

.40 .60

50 60

2 3

40 BOYS 60 GIRLS

EG:

IN A SOLUTION 20 % MILK IN B SOLUTION 30% MILK 14 LETERS FIRST SOLUTION IS WITH

X LITERS OF B SOLUTION THEN NEW SOLUTION FORMED IN THAT SOLUTION 28% MILK

FIND X?

1 2

20% 30%

28%

2 8

1 4

1 PART 14 L

4 PARTS 56

EG:

ANAND BAUGHT 2 ITEMS WITH 500 RE ON FIRST ITEM 10% ON SECOND ONE 20% THEN HE GOT OVERALL PFROFIT

OF 14% ON THOSE TWO ITEMS FIND WITHHOW MUCH COST HE BAUGHT THOSE TWO ITEMS?

1 2

10 20

6 4

RS 50O 3 2

300 200

EG:

PRAMOD BAUGHT 2 ITEMS FOR RS 500 RE HE SOLD FIRST ITEM FOR 10% PROFIT AND 2 ND ITEM FOR 5% LOSS THEN

OVERALL NO LOSS AND NO GAIN ON TWO ITEMS THEN FIND WITH HOW MUCH COST HE HE BOUGHT THOSE TWO ITEMS?

10% PROFIT 5% LOSS

110% 95%

100%

5% 10%

1 2

3 PARTS = 600

1 PART = 200

EG:

SIDDHU DIVIDED 600RS INTO TWO PARTS FIRST PART HE LENDED AT THE RATE OF 3%

2ND PART LENDED AT THE RATE OF 6% THEN HE GOT TOTAL INTEREST 300 RS

FIND THE AMOUNT LENDED FOR 3%?

600RS

1% = 60

3% 180

6% 360

1 2

180 360

300

60 120

1 2

1 PART 2000

3 PART 6000

EG:

IN A TOWN 35000 POPULATIUON 6% MALE AND 4 % FEMALE INCREASED THEN TOTAL POPULATION INCREAED TO 36766 THEN FIND

HOW MANY MALE AND HOW MANY FEMALE?

MALE FEMALE

6% 4%

2100 1400

1760

360 340

18 17

35000 = 35PARTS

1 PART = 1000

18000 17000

IN A GARDEN SOME HENS AND SOME GOATS

TOTAL HEADCOUNT IS 60 AND TOTAL LEGS IS 150 THEN FIND TOTAL HENS AND TOTAL GOATS?

HEADS LEGS

ASSUM TOTAL HENS 120 240 TOTAL GOATS

120 240

150

90 30

3 1

4 PARTS 60

1 PART 15

GOAT 15 HENS 45

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