The document discusses ratios and comparing quantities. It states that ratios are used to compare two quantities of the same kind and unit, by expressing their relative magnitudes as a fraction. Ratios must have the same units. Examples are provided to demonstrate how to set up and compare ratios, including converting units to the same type before setting up the ratio. Equivalent ratios that represent proportions are also discussed.

3. IN OUR DAILY LIFE ,THERE ARE MANY OCCASIONS WHEN WE
COMPARE TWO QUANTITIES.GENERALLY, WE COMPARE TWO
QUANTITIES EITHER BY FIND THE DIFFERENCE OF THEIR
MAGNITUDES OR BY FIND THE DIVISIONS OF MAGNITUDES.WHEN WE
WANT TO SEE HOW MUCH MORE ONE QUANTITY IS LESS THAN THE
OTHER WE FIND THE DIFFERENCE OF THEIR MAGNITUDESAND SUCH
A COMPARISON IS KNOWN AS COMPARISON BY DIFFERENCE.IN,FACT
WHEN WE COMPARE TWO QUANTITIES OF SAME KIND OF DIVISION ,
WE SAY THAT WE FORM A RATIO OF TWO QUANTITIES.

5.  RATIO IS USED WHEN WE HAVE TO COMPARE TWO
QUANTITIES .
THE RATIO OF TWO QUANTITIES OF SAME KIND AND OF
SAME UNIT IS A FRACTION THAT SHOWS HOW MANY
TIMES IS A ONE QUANTITY OF OTHER.
TO COMPARE TWO QUANTITIES ,THE UNITS MUST BE
THE SAME

7. EXAMPLE
QUES. FIND THE RATIO OF 3KM TO 300M
SOL. FIRST CONERT BOTH THE DISTANCES TO SAME
UNIT.
3KM= 3 X 1000M=3000M
THUS,THE REQUIRED RATIO, 3KM:300M IS 3000 : 300 =
10 : 1

8. SOME MORE EXAMPLES

10. COMPARISON OF RATIOS
STEP 1 OBTAIN THE GIVEN RATIOS
STEP 2 EXPRESS EACH OF THEM IN THE FORM OF FRACTION .
STEP 3 FIND THE L.C.M. OF THE DENOMINATORS OF THE FRACTIONSOBTAINED IN STEP 2.
STEP 4 OBTAIN FIRST FRTACTIOS AND ITS DENOMINATOR.DIVIDE THE L.C.M. OBTAINED IN
STEP 3 BY DENOMINATOR TO GET NUMBER X.
NOW MULTIPLY THE NUMERATOR AND DENOMINATORS OF A FRACTION BY
X. APPLY THE SAME PROCEDURE TO THE OTHER FRACTION.
NOW , THE DENOMINATORS OF ALL THE FRACTIONS WILL BE SAME.
STEP 5 COMPARE THE NUMERATORS OF FRACTIONS OBTAINED IN STEP 4 . THE FRACTION
HAVING LARGER NUMERATOR WILL BE LARGER THAN THE OTHER

11. EXAMPLE
EXAMPLE. COMPARE THE RATIOS 5 : 12 AND 3 : 8.
SOLUTION WRITING THE GIVEN RATIOS AS FRACTIONS ,
WE HAVE
5 : 12 = 5/12 AND 3: 8 = 3/8
NOW LCM OF 12 AND8 IS 24 .
5/12 = 5X2/12X2 = 10/24 AND 3/8 = 3X3/8X3 = 9/24.
THEREFORE,10/24 IS GREATER THAN 9/24 = 5/12 IS
GREATER THEN 3/8.

12. EQUIVALENT
RATIOS

13. EQUIVALENT RATIOS

16. .
WHEN TWO RATIOS ARE EQUIVALENT THEN THE FOUR
QUANTITIES ARE SAID TO BE IN PROPORTION.
1 : 2 AND 4: 8 ARE EQUIVALENT TO EACH OTHER THEN
1,2,4,8 ARE IN PROPORTION.

17. CONSIDER THE TWO RATIOS 6 : 18 AND 8 : 24. WE FIND THAT
6: 18 = 1:3 AND 8:24= 1 : 3.
6:18= 8:24
THUS, 6 : 18 = 8 : 24 IS A PROPORTION.
SIMILARLY 40 : 70 = 200 : 350, 180 : 135 = 4 : 3 ETC. ARE PROPORTIONS'
FOUR NUMBERS A ,B, C, D ARE SAID TO BE IN PROPORTION, IF THE RATIO OF
THE FIRST TWO IS EQUAL TO THE
RATIO OF THE LAST TWO, I.E., A : B = C : D .
IN FOUR NUMBERS A,B, C, D ARE IN PROPORTION' THEN WE WRITE
A:B:: C:D

20. UNITARY METHOD IS IN WHICH WE FIRST FIND THE VALUE
ONE OF ARTICLE FROM THE VALUE OF GIVEN NUMBER OF
ARTICLES AND THEN WE USE IT TO FIND THE VALUE OF
REQUIRED NUMBER OF ARTICLES.

22. EXAMPLE
THE CAR THAT RAVISH OWNS CAN GO 150 KM IN 15 LITRES OF PETROL. HOW FOR CAN IT
GO WITH 50 LITRES OF PETROL?
SOL. IT IS GIVEN THAT:
WITH 15 LITRES OF PETROL THE EAR GOES 150 KM
WITH 1 LITRE OF PETROL THE CAR GOES = 150
15
HENCE, WITH 50 LITRES OF PETROL IT WOULD GO
[150/15X50] KM=(10X50)KM=500KM

26. WHEN WE SAY THAT A MAN GIVES 30% OF HIS INCOME AS
INCOME TAX , THIS MEANS THAT HE GIVES RS.30 OUT OF
EVERY HUNDRED RUPEES OF HIS INCOME.

27. A BOY SCORED 70% MARKS IN HIS FINAL EXAMINATION
MEANS THAT HE OBTAINED 70 MARKS OUT OF EVERY
HUNDRED MARKS.

28. PER CENT AS A FRACTION
PER CENT MEANS PER HUNDRED OR HUNDREDTHS.
NOW,
75/100 = 75X1/100=75 HUNDREDTHS = 75 PER HUNDRED = 75%
AND, 42/100=42Z1/100=42 HUNDREDTHS = 42 PER HUNDRED = 42%
IT FOLLOWS FROM THIS THAT :
A FRACTION WITH ITS DENOMINATOR 100 IS EQUAL TO THAT
PERCENT, AS THE NUMERATOR.

29. PER CENT AS A RATIO
PER CENT CAN BE TREATED AS FRACTION
WITH ITS DENOMINATOR AS 100.THUS,WE HAVE
11% = 11/100
BUT , 11/100 = 11:100
11% = 11 : 100

31. STEP 1 OBTAIN THE GIVEN PERCENT. LET IT BE X%.
STEP 2 DROP THE PER CENT SIGN AND DIVIDE THE
NUMBER BY HUNDRED. THUS, X%=X/100.

35. IN OUR DAY TO DAY LIFE WE BUY GOODS FROM THE
SHOPKEEPERS IN THE MARKET WHICH THEY BUY EITHER
DIRECTLY FROM MANUFACTURERS OR WHOLESALERS. IN
ORDER TO EARN MONEY, THE SHOPKEEPERS SELL GOODS
AT A RATE I.E. HIGHER THAN THE RATE AT WHICH THEY
BOUGHT THEM. THE PRICE AT WHICH A SHOPKEEPER BUYS
THE GOODS IS CALLED ITS COST PRICE.

36. COST PRICE
THE MONEY PAID BY SHOPKEEPERS
TO BUY A GOOD FROM A
MANUFACTURER OR A
WHOLESALER IS CALLED A COST
PRICE OF THE SHOPKEEPER AND IS
ABBREVIATED BY C.P.

37. SELLING PRICE
A PRICE AT WHICH A
SHOPKEEPER SELLS THE GOOD
IS CALLED THE SELLING PRICE
OF SHOPKEEPER AND
ABBREVIATED AS S.P.

39. IF THE S.P OF AN ARTICLE IS GREATER THAN C.P. THEN A
SHOPKEEPER MAKES A GAIN OR PROFIT .
.
PROFIT = S.P – C.P
= S.P.=PROFIT C.P AND, C.P. = S.P – PROFIT.

40. IF THE SELLING PRICE OF ARTICLE IS LESS THAN THE COST
PRICE THEN A SHOPKEEPER SUFFERS A LOSS
LOSS = C.P – S.P.
= S.P=C.P. – LOSS AND,C.P.=S.P. PROFIT

43. PROFIT PER CENT = PROFIT/C.P. X 100
LOSS PERCENT= LOSS/C.P.X 100

46. GENERALLY IN TRANSACTION INVOLVING LARGE SUMS OF
MONEY SUCH AS BUYING A HOUSE OR A CAR ETC. WE
BORROW MONEY EITHER FROM A BANK OR AN INDIVIDUAL
OR SOME OTHER AGENCY. THE BANK OR AN INDIVIDUAL OR
SOME OTHER AGENCY FROM WHICH WE BORROW MONEY
IS CALLED THE LENDER AND THE PERSON OR A COMPANY
WHO BORROWS MONEY IS CALLED THE BORROWER.

47. WHAT IS LOAN?
THE MONEY BORROWED FROM ANY
FINANCIAL INSTITUTIONS IS KNOWN
AS LOAN.THE AMOUNT OF LOAN MAY
BIG OR SMALL DEPENDING UPON THE
REQUIREMENT OF THE BORROWER.

48. IMPORTANT
TERMS

49. PRINCIPAL
THE MONEY
BORROWED BY
BORROWER
FROM A
LEADER IS
KNOWN AS
PRINCIPAL OR
SUM,
INTEREST
THE ADDITIONAL
MONEY PAID BY
BORROWER TO
LENDER FOR
HAVING USED
HIS MONEY.
AMOUNT
THE TOTAL
MONEY WHICH
BORROWER
PAYS BACK TO
LENDER AT THE
END OF THE
SPECIFIED
PERIOD.

50. SIMPLE INTEREST
IF INTEREST IS CALCULATED UNIFORMLY
ON THE ORIGINAL PRINCIPAL
THROUGHOUT THE LOAN PERIOD , IT IS
CALLED SIMPLE INTEREST.

52. IF RS. P IS THE PRINCIPAL AND INTEREST RATE IS R% PER
ANNUM,THEN
INTEREST ON RE 1 FOR T YEARS= RS R/100XT
HENCE,INTEREST ON RS P FOR T YEARS =
RS[R/100 X T X P]=RS PXRXT/100.

56. MADE BY:
ABHINANDAN
VII A
ROLL NO. 02