Ratio and Proportion is one of the easiest topics of Aptitude. Usually, questions asked from this section are extremely easy. In the end, it all depends on how fast you can solve the problems.
Ratio means the number of times one quantity contains another quantity. However, the quantities in question should be of same type. You can’t do a ratio between 2 liters of oil and 6gm of gold because they are quantities of different types. A ratio of 2 liters of oil can be done with 6 liters of oil.
Ratio is expressed in the format A:B or A/B.
In A:B, A is called antecedent and B is called consequent.
Types of Ratio:
- Duplicate Ratio: This ratio is the square of two numbers. Example: 25:4 is the duplicate ratio of 5:2.
- Triplicate Ratio: This ratio is the cube of two numbers. Example: 125:8 is the triplicate ratio of 5:2.
- Sub-duplicate Ratio: This ratio is the square root of two numbers. Example: 5:2 is the sub-duplicate of 25:4
- Sub-triplicate Ratio: This ratio is the cube root of two numbers. Example: 5:2 is the sub-duplicate of 125:8
- Inverse Ratio: The ratio in which antecedent and consequent change their places. Example: 25:4 is the inverse of 4:25.
Two ratios are said to be in Proportion when they are equal. For example: 2/5 = 4/10.
This is because 4/10 can be divided by 2 and can be simplified as 2/5. Hence, 2/5 and 4/10 are said to be in proportion. In the equation A:B = C:D, A and D are called extremes, whereas B and C are called means.
In a proportion, product of means is always equal to product of extremes.
In other words, for proportion A:B = C:D;
AD = BC
Types of Proportions:
- Forth Proportion: When a:b = c:d, then d is called the forth proportion of a,b and c.
- Third Proportion: When a:b = b:c, then c is called the third proportion of a and b.
- Second Proportion: When a:b = b:c, then b is called second or mean proportion of a and c.
Enough with the theory. Moving on to….
Shortcut 2: When A : B = m : n, B : C = p : q, and C : D = r : s. Then A : B : C : D = mpr: npr : nqr : nqs
Question 1: If A:B = 2:3, B:C = 3:4, C:D = 4:5, find A:B:C:D?
Solution 1: 2x3x4: 3x3x4: 3x4x4: 3x4x5 = 24:36:48:60 (Try to solve this mentally)
Shortcut 3: In a container, the ratio between oil and water is P:Q. The total quantity is x litres. To find the amount of water to be mixed so that the ratio becomes A:B, use
x(pb – qa)
a(p + q)
I'm Dushyant Shrivastava, A Professional blogger from Hyderabad, currently in Bangalore.
My niche is teaching stuff about IBPS and SBI competitive exams. I mostly talk about preparation tutorials, and occasionally about some recent exam notifications. You may visit my site at BankersAmbition.com to get a glimpse of my writings.
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