Banks SSC - Ratio, Proportion and Variation

1. Bank Exams and SSC
Concept Session 1: Ratio, Proportion and Variation
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2. Basic Concepts
Ratio – Introduction and Terminology
Ratio - Properties
Combining ratios
Proportion – Properties
Variation – Properties
Supplementary Topics
Comparison of fractions – Part 1
Comparison of fractions – Part 2
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Ratio, Proportion and variation 2

3. Ratio, Proportion and Variation – Session 1
• Ratio – Introduction and Terminology
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4. Ratio – What is it?
 Ratio: Comparison of magnitude of two quantities.
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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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Answers:
- Rs. 10,000
- Rs. 8000

5. Ratio – Problems on basic understanding
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What is the value of A:B:C ? If,
a) A:B:C =
1
3
∶
1
2
∶
1
5
b)
A
3
=
B
2
=
C
5
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Answers:
a) 10 : 15 : 6
b) 3 : 2 : 5

6. Ratio – Terminology
Terminology
 Antecedent and consequent
 Let the ratio of A’s age and B’s age = a:b
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Duplicate ratio of their ages 𝑎2: 𝑏2
Triplicate ratio of their ages 𝑎3: 𝑏3
Sub-duplicate ratio of their ages 2
𝑎:
2
𝑏
Sub-triplicate ratio of their ages 3
𝑎:
3
𝑏

7. Ratio – Terminology
⁻ If 5a+2 : 12a+4 is the triplicate ratio of 3:4, what is the
value of a?
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Answer: 5

8. Ratio, Proportion and Variation – Session 1
• Ratio – Properties
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9. Ratio – Properties
Properties of Ratios
Value of ratios when multiplied or divided by the same
number remains the same
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10. Ratio – Properties
Properties of Ratios
Change of values of proper and improper fractions when the same value is
added or subtracted to the Nr and the Dr.
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Proper Fraction Improper Fraction
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11. Ratio – Properties
Properties of Ratios
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
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12. Ratio – Properties
Properties of Ratios
• 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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13. Ratio – Properties
Properties of Ratios - 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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14. Ratio – Properties
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If
𝑎+𝑏
𝑐
=
𝑏+𝑐
𝑎
=
𝑎+𝑐
𝑏
= p, what is the value of p?
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1) 2
2) -1
3) -2
4) 3
5) Either 1 or 2
Answer : Option 5

15. Ratio, Proportion and Variation – Session 1
• Combining Ratios
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16. Ratio – Combining ratios
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17. Ratio – Problems
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If A:B = 3:1, C:B = 2:1, C:D = 1:3 what is the
value of A:D?
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1) 1:2
2) 2:1
3) 1:3
4) 3:1
5) None of these
Answer : Option 1

18. Ratio – Problems
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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?
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1) 200
2) 25
3) 12.5
4) 30
5) 50
Answer : Option 3

19. Ratio – Problems
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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
(a) 5
(b) 10
(c) 15
(d) 20
(e) 25
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Answer : Option a

20. Ratio – Problems
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The ratio between the boys and girls in a class is 6: 5
respectively. If 8 more boys join the class and two girls leave
the class then the respective ratio becomes 11: 7. What is
the number of girls in the class now?
(a) 28
(b) 38
(c) 45
(d) 36
(e) 30
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Answer : Option e

21. Ratio – Problems
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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
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Answer : Option 4

22. Ratio, Proportion and Variation – Session 1
• Proportion – Properties
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23. Proportion – What is it?
 What is a proportion?
 Product of extremes = product of means
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24. Proportion – Continued Proportion
 If a:b =b:c, then a,b and c are in continued
proportion.
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25. Proportion – Problems
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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.
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1) 24
2) 12
3) 20
4) 40
5) 64 Answer : Option 40

26. Proportion – Problems
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Find the fourth proportional to 1, 3 and 4
1) 12 2) 24 3) 18 4) None of these
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Answer : Option 1

27. Ratio, Proportion and Variation – Session 2
• Variation – Properties
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28. Variation – Direct variation/proportion
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Direct Relation Vs Direct Variation
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29. Variation – Inverse variation/proportion
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30. Variation – Joint variation/proportion
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31. Variation – Problems
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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?
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Answer : Option 1
1) 20
2) 15
3) 24
4) 30
5) 16

32. Variation – Problems
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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?
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Answer : Option 3
1) 200
2) 750
3) 700
4) 300
5) 160

33. Variation – Problems
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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?
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1) 2
2) 4
3) 3
4) 1
5) None of these Answer : Option 1