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Ratio - Introduction
Ratio: Comparison of magnitude of two
or more quantities.
Example Problem:
The ratio of the expenses of A and B is 5:9. If the sum of
their expenses is Rs. 28000.
-What is A’s expense?
-By how much is B’s expense greater than A’s expense?
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Ratio - Terminology
• Antecedent and consequent
Ratio of a and b 𝒂 ∶ 𝒃
Duplicate ratio of a and b 𝑎2
∶ 𝑏2
Triplicate ratio of a and b 𝑎3
∶ 𝑏3
Sub-duplicate ratio of a and b 2
𝑎:
2
𝑏
Sub-tuplicate ratio of a and b 3
𝑎:
3
𝑏
Antecedent Consequent
𝑎 ∶ 𝑏
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Ratio - Properties
Change of values of proper and improper fractions when
the same value is added or subtracted to the Numerator
and the Denominator.
Proper Fraction
(fractions of the form 𝑝/𝑞, where 𝑝 < 𝑞)
Improper Fraction
(fractions of the form 𝑝/𝑞, where 𝑝 ≥ 𝑞)
𝑝
𝑞
<
𝑝 + 𝑥
𝑞 + 𝑥
, 𝑥 > 0
𝑝
𝑞
>
𝑝 + 𝑥
𝑞 + 𝑥
, 𝑥 > 0
𝑝
𝑞
>
𝑝 − 𝑥
𝑞 − 𝑥
, 𝑥 > 0
𝑝
𝑞
<
𝑝 − 𝑥
𝑞 − 𝑥
, 𝑥 > 0
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Ratio – Properties (Summary)
• Value of ratios when multiplied or divided by the same number
remains the same
• Change of values of proper and improper fractions when the same
value is added or subtracted to the Nr and the Dr.
• If
𝑎
𝑏
=
𝑐
𝑑
=
𝑒
𝑓
……. then
𝑎 + 𝑐 + 𝑒 +⋯
𝑏+𝑑+𝑓+⋯
= each of
𝑎
𝑏
,
𝑐
𝑑
… As long as (𝑏 +
𝑑 + 𝑓 + ⋯ ) ≠ 0
• Given
𝑎
𝑏
,
𝑐
𝑑
,
𝑒
𝑓
, the value of
𝑎+𝑐+𝑒
𝑏+𝑑+𝑓
will be between the lowest and
highest fraction.
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Problems
A has thrice the amount of money that B has, B has twice the amount
of money that C has and thrice the amount of money with C is equal
to four times the amount of money with D. The amount of money with
D is what percentage of the amount of money with A?
1) 200
2) 25
3) 12.5
4) None of these
Answer: option 3
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Proportion – Continued Proportion
𝑎, 𝑏 and c are in continued proportion if
Third proportional
𝑎: 𝑏 = 𝑏 ∶ 𝑐
𝑏 = 2
𝑎𝑐
Second Proportional (or)
Mean Proportional
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Problems
Ratio of 𝑝: 𝑞 is the same as that of 𝑞: 𝑟, where 𝑝, 𝑞 and 𝑟 are positive
numbers. If 𝑝 = 16 and 𝑟 = 100, find 𝑞.
1) 40
2) 64
3) 24
4) None of these
Answer: option 40
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Problems
4 men working 5 hours a day can complete 4 units of work in 48 days. In how
many days will 12 men working 6 hours a day complete a work of 6 units?
1) 20
2) 15
3) 24
4) 16
Answer: option 1
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Problems
A garrison of 2200 men has ration for 16 weeks at the rate of 60gms per day
per man. How many must leave the garrison if the ration should last for 32
weeks at the rate of 44gms per day per man?
1) 200
2) 750
3) 700
4) 6
Answer: option 3
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Problems
In a hostel of 400 students, there was ration for 15 days. After 5 days, 100
more students join the hostel. If each student consumes at the same rate, for
how man days will there be a shortage of ration?
1) 2
2) 4
3) 1
4) 3
Answer: option 1
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Problems
70 cows can graze on a field for 24 days and 30 cows can graze on the same
field for 60 days. Some grass is already there and grass grows at a fixed rate.
How many cows can graze on the field for 96 days?
1) 20
2) 25
3) 18
4) None of these
Answer: option 1
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Problems
A boy has a few coins of denominations 50 paise, 25 paise and 10 paise in the
ratio 1: 2: 3. If the total amount of the coins is Rs. 6.50, the number of 50
paise coins is
1) 5
2) 10
3) 15
4) 20
5) 25
Answer: option 1
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Problems
In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be
1 : 2, then the quantity of water to be further added is
1) 20 liters
2) 30 liters
3) 50 liters
4) 60 liters
5) 80 liters
Answer: option 4
