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Techniques for Ratio
Eg 1. 2/1352 is close to the ratio 1/676
Eg 2. Find the ratio closest to 14.37/241 ?
(a) 3/32 (b) 4/67 (c) 7/11 (d) 5/81
Sol:
Eg. 3. Which is the highest ratio among ^{13}/_{447},^{45}/_{508},^{28}/_{583},^{18}/_{531}?
Sol:
Step 1: Reverse the position of the upper value(numerator) and the lower value(denominator).
Step 2 : Take the closest value
Step 3 : the maximum value is the minimum ratio and minimum value is the maximum ratio.
Eg. 4. Which is the highest ratio among ^{471}/_{525} , ^{324}/_{411} , ^{648}/_{749} ?
Sol:
S1: Approximate the given ratio (if the no. of digits in numerator/denominator is more than 2 )
S2: Multiply the numerator by 10 and get the result fractionS3: Find only the integer value of the result fraction
S4: If any of the integer value of the result fractions is same then find the next decimal places and so on.
S5: Compare the value of the result fractions. The maximum ratio will have maximum value.
Eg 5. Consider , 31/83, 15/46, 22/65, then it is required to find which of the among ratio is less than 1/3 ?
Sol:
Techniques for Percentage
Case 1. To find by how much per cent X is more or less than Y compared to Y.
Example:
ExampleIf A's income is 20% more than B, then how much % B's income is less than that of A's income ?
Sol:
^{20}/_{120}×100
Example
Example
1+10/100=110/100
^{20}/_{120}×100
Case 2. To find the percentage change in any value in year M compared to that value in year K.
The total population of a village is 5000.The number of males and females increases and consequently the population of the village becomes 5600.Find the percentage change in the population?
Sol:
^{600}/_{5000}×100 = 12%
Case 3. To find the original value if the value after its x% increase or decrease is known
Rakesh's salary is increased by 10% and he get now Rs. 5000. Find his salary before the increase ?
Sol:1+10/100=110/100
^{5000}/_{110}×100 = 4545.45
Case 4. Two percentage value cannot be compared unless the base values are known.
Example
6% of income of Ram is equal to 18% of income of Shyam 10% of income of Shyam is equals to 30% of income of Mohan. Find the total income of Ram, Shyam and Mohan ?
Sol:
Cannot be determined.
Case 5. Two percentage values can be compared in terms of percentage values ( but not in absolute values) when the base values are same ( although base values are not known ) .
Example
A's height is 40% less than that of B, how much percent B's height is more than that of A ?
Sol:
Let A = 60 and B = 100
40/60×100 = 66^{2}/_{3}%
Case 6. To find the value of a parameter in any year K when the % change in its value over two different periods( any period having the year K) are same.
Example
Techniques for Average
Examples
(1) Find the average annual production increase in product over the period 2000 to 2004 ?
% increase in Production during 2000  2004 = 4525/25×100 = 80%
Average % increase during 200004 = 80/5 = 16%
(2) The data of sale of a Company in the different years of its product type x,y,z are as below :
Year  X  Y  Z  Total 
2001  8  4  30  42 
2002  16  16  18  50 
2003  18  32  24  74 
2004  14  21  20  55 
2005  18  16  28  62 
(a) In which of the given years the sale of product Z was close to its average sale over the years?
Sol:(30+18+24+20+28) = 120
120/5 = 24
So, the year which is closest to the average is 2003.
(b) In which of the given years the sale of product Z was close to its average sale of all the products in the year ?
Sol:Year  Average Sale  Sale of Product Z  Difference 
2001  42/5 = 8.4  30  Difference with average 308.4 = 21.6 is very wide, so calculation not required 
2002  50/5 = 10  18  18  10 = 8 
2003  74/5 = 14.8  24  2414.8 = 9.2 
2004  55/5 = 11  20  2011 = 9 
2005  62/5 = 12.4  28  Difference with average = 2812.4 = 15.6 is very wide, so calculation not required 
(c) Production and Exports of Pulses (In Million kg) has been given below
Year  200001  200102  200203  200304  200405 
Exports  114  115  220  180  310 
Production  242  340  640  565  930 
Find the average proportion of pulses exported as a fraction of the tea produced in the half decade was (a) 0.11 (b) 0.22 (c) 0.36 (d) 0.41 (e) 0.49
Sol: Here none of the given choices are closer to each other, so mental calculation may work. Just observe that exports are generally ^{1}/_{3}rd of production with one year (199091) showing nearly 1/2 of production as exports. Hence the required average will be > 1/3 ( = 0.33). Thus 0.36 looks the closest among the alternatives given.(d) Sectoral Growth Rate of Major Industry Groups (201516) are given as
Sectors  Weights  20152016 
Oil  56.6  6.5 
Pulses  24.4  7.5 
Books  19  8 
Overall  100.00 
Find the overall weighted industrial growth rate in 201516 ?
Sol:Weighted average of X = (w_{1}x_{1}+w_{2}x_{2}+w_{3}x_{3})/(w_{1}+w_{2}+w_{3})
Required weighted average growth rate in 200102 = (56.6×6.5+24.4×7.5+19×8)/(56.6+24.4+19)
= 702.9/100
= 7.03
Example
Directions(15): Study the following table and answer the questions given below in
Production of different types of pulses in a company(figures in thousand)
Year

Types of pulses
 
A

B

C

D

E
 
2002

180

60

84

100

76

2003

210

90

32

80

48

2004

135

30

44

95

85

2005

190

85

69

125

115

2006

260

95

120

80

120

2007

240

140

161

90

185

1. In which of the given years was the production of Btype pulses close to its average production over given years?
(a) 2005 (b) 2004 (c) 2003 (d) 2002 (e) None
2. In which year the production of Dtype pulses was maximum ?
(a) 2003 (b) 2006 (c) 2005 (d) 2007 (e) 2002
3. What was the approximate percentage of production of Atype pulses in 1995 to its total pulses over the years?
(a) 20 (b) 15 (c) 23 (d) 40 (e) 30
4. In which of the following pairs of years was the total production of Etype pulses two lakhs?
(a) 2003 & 2005 (b) 2005 & 2007 (c) 2004 & 2007 (d) 2002 & 2004 (e) None
5. In which of the given years the total production of all types of scooters was minimum ?
(a) 2004 (b) 2006 (c) 2007 (d) 2005 (e) None
Solution
S1 (a)average production of Btype pulses over the years (20022007) =^{(60+90+30+85+95+140)}/_{6}
= 83 (in thousand)
S2 (c)
S3 (b)
Approximate percentage of production of Atype pulses in 2005 to its total production
= ^{Production in 2005 of Atype}/_{Total production of Atype (200207)}×100
= ^{190}/_{(180+210+135+190+260+240)}×100
= ^{190}/_{1215}×100
= 15
S4 (e)
Pairs of years  Total production of Etype pulses 
2003 & 2005  48 + 115 ≠ 
2005 & 2007  115 + 185 ≠ 
2004 & 2007  85 + 185 ≠ 
2002 & 2004  76 + 84 ≠ 
S5 (a)
Year  Total Production of all types pulses 
2002  180 + 60 + 84 + 100 + 76 = 500 
2003  210 + 90 + 32 + 80 + 48 = 460 
2004  135 + 30 + 44 + 95 + 85 = 389 → Minimum 
2005  190 + 85 + 69 + 125 + 115 = 444 
2006  260 + 95 + 120 + 80 + 120 = 675 
2007  240 + 140 + 161 + 90 + 185 = 816 
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