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, Table of Contents

Ratio and Proportion
Partnership Mixtures
and Allegation Average
Percentage Profit,
Loss and Discount
Problems on Ages Time,
Speed and Distance
Trains
Boats Time
and Work Pipes
and Cisterns
Simple and Compound Interest
Number System HCF
and LCM Heights and
Distances Progressions
Calendar
Clocks
Permutation and Combination
Probability
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, Shortcut # 1 - Ratio and Proportion
Splitting a number in the given ratio.

1. Divide 720 in the ratio 2: 3.




Solution 1:
Total parts = 2 + 3 = 5
First number = (2/5) 720 = 288
Second number = (3/5) 720 = 432

Solution 2:
2x + 3x = 720; 5x = 720; x = 144
2x = 2(144) = 288; 3x = 3(144) = 432

2. Divide 720 in the ratio 2: 3: 4.




Solution 1:
Total parts = 2 + 3 + 4 = 9
First number = (2/9) 720 = 160; Second number = (3/9) 720 = 240; Third
number = (4/9)720 = 320

Solution 2:
2x + 3x + 4x= 720; 9x = 720; x = 80
2x = 2(80) = 160; 3x = 3(80) = 240; 4x = 4(80) = 320

, Shortcut # 2 – Ratio and Proportion
Direct Proportion.

When two parameters are in direct proportion if one parameter
increases the other one will also increase and if one parameter decreases
the other one will also decrease.
If the parameters A and B are in direct proportion they will satisfy the
below equation.




Question:
Price of diamond is directly proportional to its weight. If 2 grams of diamond
costs $ 45,000 then what is the price of a diamond that weighs 6 grams?
Answer:
Weight of diamond in first case, A1 =2
Weight of diamond in second case, A2 =6
Price of diamond in first case, B1 = 45000
Price of diamond in second case, B2 =?

According to the equation,

2/6 = 45000/B2

B2 = 45000 x (6/2)

B2 = 135,000