## Ratio and Proportion Formulas

**Ratio:** The ratio of two quantities a and b in the same units, is the fraction and we write it as a : b.

In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent.

**Example:** The ratio 5 : 9 represents with antecedent = 5, consequent = 9.

**Rule:** The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.

Eg. 4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.

**Proportion:** The equality of two ratios is called proportion.

If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion.

Here a and d are called extremes, while b and c are called mean terms.

**Product of means** = Product of extremes.

Thus, a : b :: c : d (b x c) = (a x d).

**Fourth Proportional:** If a : b = c : d, then d is called the fourth proportional to a, b, c.

**Third Proportional:** a : b = c : d, then c is called the third proportion to a and b.

**Mean Proportional:** Mean proportional between a and b is ab.

**Comparison of Ratios:** We say that (a : b) > (c : d)

**Compounded Ratio:** The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf).

**Duplicate Ratios:** Duplicate ratio of (a : b) is ( : ).

Sub-duplicate ratio of (a : b) is (a : b).

Triplicate ratio of (a : b) is : )..

Sub-triplicate ratio of (a : b) is

If , then [componendo and dividendo]

**Variations:** We say that x is directly proportional to y, if x = ky for some constant k and we write, x ∞ y.

We say that x is inversely proportional to y, if xy = k for some constant k and we write, x ∞

## Ratio and Proportion Important Examples

**Example: 1**. A and B together have Rs. 1210. If of A's amount is equal to f B's amount, how much amount does B have?

**Answer: 484**

**Explanation:**

B's share = Rs.

**Example 2:** A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

** Answer:** 2000

** Explanation:** Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.

Then, 4x - 3x = 1000

x = 1000.

B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

**Example 3:** Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

** Answer:** 2 : 3 : 4

** Explanation:** Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.

Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).

The required ratio =

14x : 21x : 28x

2 : 3 : 4

**Example 4:** 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:

** Answer:** 60 litres.

** Explanation:** Quantity of milk = litres = 40 litres.

Quantity of water in it = (60- 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres.

Then, milk : water =

20 + x = 80

x = 60.

Quantity of water to be added = 60 litres.

## Ratio and Proportion Questions from Previous Year Exams

IBPS Questions Related to Ratio and proportion.

## Ratio and Proportion Video Lecture

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