# Ratio and Proportion : Problems, Formulas, and Shortcuts

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….

**SHORTCUTS: **

**Shortcut 1: ****When A : B = m : n, and B : C = p : q. Then A : B : C = mp : pn :nq**

Question 1: If A:B = 2:3 and B:C = 4:5, find A:B:C?

Solution 1: A:B:C = 2×4: 3×4: 3×5 = 8:12:15

Question 2: If A:B = 5:3 and B:C = 6:2, find A:B:C?

Solution 2: A:B:C = 30:18:6 (Try to solve this mentally. Its very easy)

**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)

Question 1: A container has oil and water in the ratio 2:3. The total quantity of oil and water is 10 liters. What amount of water should be added, so that the ratio becomes 1:3?

Solution 1: Solving by formula,

Amount of water to be added = __10 (2×3 – 3×1)__ = __10 (6-3)__ = 6 liters

1 (2+3) 5

(More shortcuts coming soon)

Hi, I can’t really understand the last part. Though if the readers are willing to know another solution which is not really a kinda shortcut but wants to know the answer, here is how I got the final answer for shortcut 3.

1st part:

Given ratio: 2:3

Total Quantity: 10 litres

sol’n:

2+3=5 (use the sum to divide the total)

10÷5=2 (use the quotient to multiple to each ratios)

2×2:2×3 = 4:6 (this is the exact ratio)

Part 2:

Ratio to be solved: 1:3

“What amount of water should be added?” (This a word prob equation key words)

4:6 from first part (oil:water) and equate to the given ratio

4/6+x =1/3 (cross multiply)

4×3 =6+x

12=6+x

12-6=x

x=6 (now substitute it to x)

4/6+x

4/6+(6)

4/12 (FINAL ANSWER)

If you simplified further, it will be 1/3

here ya go.

Kaway Kaway sa kukuha sa admu, dlsu, ust saka up!

-v

Please keep formulas

shortcut 3 is not understand

i dont know how you defined.

3:27::6:216

explanation: 3^3=27 & 6^3=216 so answer is 216

or

3*9=27 & 6*9=54 based on the options select answer

Hi sir, can you please help me how to calculate matrix?

its really so easy and short ….so thaku so muchhhhhhh

If a:b:c 2:3:5 and a-6cm then find b and c

if we are given with a:b:c then what would be the formula? bc:ca:ab or ab:bc:ca???

It helped me a lot… thanks

hello sir,

I am preparing for bank po exams currently..I am actually finding profit loss and discounts a difficult stuff for me..Could you just provide me with some tricks and the easier ways to deal with these chapters?

It’s nice.. Sir We r expecting more.

What is the value of a in shortcut 3 .. I can’t get it clearly.. Could y explain

hope to have this website my tutoring solution

Very nice and helpfull shortcuts…thnx

3:27::6:? Plz send me the formula with explain this query.

super

hi, thank u and super

very easy and great method thank you very much dushyanth ji