# A guide to solving questions on Ratio and Proportion

Published: Published Date - 11:52 PM, Mon - 18 April 22

**Hyderabad:** Ratio and Proportion is one of the important topics for SI of Police and Police Constable exams. Minimum 3 to 5 questions will cover from this topic. Now we will discuss some basics.

**I. RATIO:**

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

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

Ex. The ratio 2 : 3 represents 2/3 with antecedent = 2, consequent = 3.

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

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

**2. PROPORTION:**

The equality of two ratios is called proportion.

If a: b = c: d, then these two ratios are in proportion. It can be written as

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 extremes = Product of means.

Thus, a: b:: c : d

Here ad = bc

3. (i) Fourth Proportional: If a: b = c: d, then d is called the fourth proportional to a, b, c.

(ii) Third Proportional: If a: b = b: c, then c is called the third proportional to a and b.

(iii) Mean Proportional: Mean proportional between a and b is square root of ab

**4. COMPOUNDED RATIO:**

The product of antecedents is to the product of consequents is known as Compound ratio of given ratios.

The compounded ratio of the ratios a: b, c: d and e: f is ace: bdf

5. (i) Duplicate ratio of a: b is a2: b2.

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

(iii)Triplicate ratio of a: b is a3: b3.

(iv) Sub-triplicate ratio of a: b is a ⅓: b ⅓.

**6. VARIATION:**

(i) We say that x is directly proportional to y, if x = ky for some constant k and we write, x y.

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

**x(1/y)**

**Ratio and Proportion Trick**

One example which can be solved in 30 sec if you use this trick

Example: If A: B = 3: 4, B: C = 2: 3 and C: D = 5: 7, then find A: B: C: D.

Solution: General method of solving this question is very lengthy, so let me tell you how can we calculate it easily.

See how it is simple, you just need to remember the pattern and if you notice it, it is really simple

Last and first steps are just the straight lines. So, what is left, just the middle pattern?

If we talk about only three terms i.e. A, B and C. Then the pattern will be much easier. Let’s see how,

**Previous year questions:**

1) Two numbers are in the ratio of 11:13. If 12 is subtracted from each, the ratio becomes 7:9. The smaller number of them is(SI 2016)

11 b) 22 c)33 d) 39

Ans: c

Explanation:

Initial ratio of two numbers = 11: 13

Final ratio of two numbers = 7: 9

The two numbers are 11x and 13x respectively

According to the question

(11x – 12)/(13x – 12) = 7/9

⇒ 9 (11x – 12) = 7 (13x – 12)

⇒ 99x – 108 = 91x – 84

⇒ 99x – 91x = 108 – 84 ⇒ 8x = 24 ⇒ x = 3

Smaller number is 11x = 33

2) The sum of three numbers is 186. If the ratio between the first and second is 2:3 and that between the second and third is 7:9, then the second number is(SI 2016)

a) 53 b) 63 c)58 d) 68

Ans: b

**Explanation:**

Let the three numbers be a, b and c respectively.

a: b = 2: 3

b: c =7: 9

Therefore, a: b: c = 2×7:3×7:3×9= 14: 21: 27

According to the question,

a b c = 186

=>; 14x 21x 27x = 186

=>; 62x = 186 =>; x = 186/62=3

Therefore, b = 21x = 21*3 = 63

3) The students in three classes are in the ratio of 2: 3: 5. If 40 students are added in each class, the ratio becomes 4: 5: 7. Find the total number of students in all the three classes is (SI 2016)

a) 100 b) 180 c) 200 d) 400

Ans: c

**Explanation:**

Let the number of students in 3 classes be 2k,3k,5k

=>; 2k 40: 3k 40: 5k 40 =>; 4:5:7

=>; 2k 40: 3k 40 = 4:5

=>; 2k 40/3k 40=4/5

=>; 10k 200 = 12k 160 =>;k = 20

∴ Number of students in 3 classes

2k,3k,5k = 40,60,100

Total = 40 60 100 = 200