RATIO
Ratio means the number of times one
quantity contains another quantity of the same kind. The comparison is made by
considering what part or multiple the first quantity of the second.
Thus the ratio between Rs 50 and Rs 200 can be possible, but not between Rs 50 and 200 marks.
The ratio between one quantity to another is measured by a : b or a/b
^{Ex}^{: 8:9 or 5:7 etc. The two quantities in the ratio are called its terms. The first is called the antecedent and the second term is called consequent. }
Thus the ratio between Rs 50 and Rs 200 can be possible, but not between Rs 50 and 200 marks.
The ratio between one quantity to another is measured by a : b or a/b
^{Ex}^{: 8:9 or 5:7 etc. The two quantities in the ratio are called its terms. The first is called the antecedent and the second term is called consequent. }
^{Types of Ratios:
}
^{1. Duplicate ratio: The ratio of the
squares of the two numbers.
}^{Ex}^{: 9 : 16 is the duplicate ratio of 3
: 4.
}
^{2. Triplicate Ratio: The ratio of the cubes
of the two numbers.
}^{Ex}^{: 27 : 64 is the triplicate ratio of
3 : 4.}
^{3. Subduplicate Ratio:}^{ The ratio between the square roots of the two numbers. Ex: 4 : 5 is the subduplicate ratio of 16 : 25. }
^{4. Subtriplicate Ratio: The ratio between the cube roots of the two numbers. Ex: 4 : 5 is the subtriplicate ratio of 64 : 125. }
^{5.Inverse ratio: If the two terms in the ratio interchange their places, then the new ratio is inverse ratio of the first. Ex: 9 :5 is the inverse ratio of 5 : 9. }
^{6. Compound ratio: The ratio of the product of the first terms to that of the second terms of two or more ratios. Ex: The compound ratio of }_{}3/4, 5/7, 4/5, 4/5 is 9/35
^{ }
^{PROPORTION }
^{If two ratios are equal, then they make a proportion. Thus }4/5 = 8/10_{} or 4:5 = 8:10
^{Each term of the ratios 4/5 and 8/10 }_{ }^{is called proportional. The middle terms 5 and 8 are called means and the end terms 4 and 10 are called extremes.}
Product of Means = Product of Extremes

^{Continued Proportion:}^{ In the proportion }_{}^{8/12= 12/8
8, 12, 18 are in the continued proportion.
}
^{Fourth proportion: If a : b = c : x, then x
is called fourth proportion of a,b and c.
There fore fourth proportion of a, b, c = }_{}b x c/a
^{ }
^{ }
^{Third proportion: If a : b = b : x,
then x is called third proportion of a and b.
Therefore third proportion of a, b = b^2/a}_{}
^{ }
^{ }
^{Second or mean proportion: If a : x = x
: b , then x is called second or mean proportion of a and b.
Therefore mean proportion of a and b = root(ab)}_{}
EXAMPLES

^{Example 1:}^{ Find out the two quantities whose
difference is 30 and the ratio between them is 5/11.
}^{Sol}^{: The difference of quantities,
which are in the ratio 5:11, is 6. To make the difference 30, we
should Multiply them by 5.
Therefore }^{5:11 = 5x5 : 11x5 = 25 : 55
}
^{Example 2: A factory employs skilled
workers, unskilled workers and clerks in the ratio 8:5:1 and the wages of a
skilled worker, an unskilled worker and a clerk are in the ratio 5:2:3 when 20
unskilled workers are employed the total daily wages fall amount to Rs. 318.
Find out the daily wages paid to each category of employees.
}^{Sol}^{: Number of skilled worker:
unskilled worker: clerks = 8:5:1 and the ratio of their respective Wages =
5:2:3
Hence the amount will be paid in the ratio
8 × 5 : 5 × 2 : 3 × 1 = 40 : 10:3}
^{ Hence total amount distributed among unskilled workers 318 x 10 / (40+10 +3)}_{}^{} = Rs 60.
^{ Hence total amount distributed among unskilled workers 318 x 10 / (40+10 +3)}_{}^{} = Rs 60.
^{Example 3: Two numbers are in the ratio of 11:13. If 12 be subtracted from each, the remainders are in the ratio of 7:9 Find out the numbers. Sol: Since the numbers are in the ratio of 11:13. Let the numbers be 11x and 13x. Now if 2 is subtracted from each, the numbers become (11x 12) and (13x12). As they are in the ratio of 7:9 (11x12): (13x12):: 7: 9 (11x – 12) 9 = (13x – 12) 7 99x – 108 = 91x – 84 9x = 24 or x = 3 Therefore the numbers are 11 x 3 = 33 and 13 x 3 = 39}

^{ = Rs. 90 }
^{Example 6: A bag contains of one rupee, 50 paise and 25 paise coins. If these coins are in the ratio of 2:3:10, and the total amount of coins is Rs288, find the number of 25 paise coins in the bag. Sol: Ratio of one rupee, 50 paise and 25 paise coins = 2:3:10 Ratio of their values = 8:6:10 = 4:3:5 And sum of the ratios of their values = 4 + 3 + 5 = 12 Value of 25 paise coins (5x288)/12 }_{}^{= Rs. 120 No. of 25 paise coins = 120 × 4 = 480 }
Nice way of solving problems...Thanx a lot..
ReplyDeletethe answer to question 4 is not appropriate.. kindly provide correct solution..
ReplyDeletesolution to question 4:
ReplyDeleteRatio of inferior quality to superior quality=(rate of superior  rate of mix)/(rate of mix rate of inferior)
= (4836)/(3632)
=12/4
=3:1
This comment has been removed by the author.
Deletethank you samuel.. i didn't see question before and checked only the answer and left it.
ReplyDeletei just checked it now.. both question and answer.. :P
Answer to Question 1 is not 25:25 ( Therefore 5:11 = 5x5 : 11x5 = 25 : 25)
ReplyDeleteCorrect Answer is 25:55 ( Therefore 5:11 = 5x5 : 11x5 = 25 : 55)