How to Solve Approximation Questions? Check important Tips & Tricks

In most of the Banking Prelims exam, the major chunk of questions is asked from the topic Approximation and Simplification. They are very easy and require good calculation skills. 

Here is a short study guide to help you crack questions on Approximation“. To solve approximation questions, you must understand the basic rules of Simplification. 

Importance of Approximation in Bank Exams?

• You can expect 5-10 approximation questions in every bank exam especially in the prelims phase.
• These questions are quite easy to solve if you have practiced well on your calculation speed.
• You can solve all the questions within 3-4 minutes with 100% accuracy.
• These questions can increase your chances of clearing the exam.

Basic Rules of Simplification

BODMAS Rule

It defines the correct sequence in which operations are to be performed in a given mathematical expression to find the correct value. This means that to simplify an expression, the following order must be followed –

B = Bracket,
O = Order (Powers, Square Roots, etc.)
D = Division

M = Multiplication
A = Addition

S = Subtraction

1. Hence, to solve approximation questions correctly, you must apply the operations of brackets first. Further, in solving for brackets, the order – (), {} and [] – should be strictly followed. 
2. Next you should evaluate exponents (for instance powers, roots, etc.)

3. Next, you should perform division and multiplication, working from left to right. (division and multiplication rank equally and are done left to right).

4. Finally, you should perform addition and subtraction, working from left to right. (addition and subtraction rank equally and are done left to right).

EXAMPLE 1: Solve 12 + 22 ÷ 11 × (18 ÷ 3)^2 – 10

= 12 + 22 ÷ 11 × 6^2 – 10 (Brackets first)
= 12 + 22 ÷ 11 × 36 – 10 (Exponents)
= 12 + 2 × 36 – 10 = 12 + 72 – 10 (Division and multiplication, left to right)
= 84 – 10 = 74 (Addition and Subtraction, left to right)

EXAMPLE 2: Solve 4 + 10 – 3 × 6 / 3 + 4

= 4 + 10 – 18/3 + 4 = 4 + 10 – 6 + 4 (Division and multiplication, left to right)
= 14 – 6 + 4 = 8 + 4 = 12 (Addition and Subtraction, left to right)

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Tips to Solve Approximation

Conversion of decimal numbers to the nearest number

To solve such questions, first, convert the decimal to the nearest value. Then simplify the given equation using the new values that you have obtained.

EXAMPLE 1: Solve 4433.764 – 2211.993 – 1133.667 + 3377.442

Here,
4433.764 = 4434
2211.993 = 2212
1133.667 = 1134
3377.442 = 3377

Now simplify, 4434 –  2212 – 1134 + 3377 = 4466

EXAMPLE 2: Solve 530 x 20.3% + 225 x 16.8%

Here, 20.3% becomes 20% and 16.8% becomes 17%
Now, simplify 530 x 20% + 225 x 17%
= 106 + 38.25 = 144.25

EXAMPLE 3: 38.97×15.02-27.94×10.02=(36+?)×4.92   As per the BODMAS rule, the priority in which the operations should be done is:

Note: Addition and subtraction can be treated on the same priority (from left to right) when they are in consecutive order.

38.97×15.02-27.94×10.02=(36+?)×4.92
Approximating the value to the nearest integer:
39×15-28×10=(36+?)×5 
585-280=(36+?)×5 
305=(36+?)×5 
=36+? 
61=36+? 
?=61-36 
?=25

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EXAMPLE 4: √483.9915 + (7.0215)² = ? *6.0212  – 1.0215³   As per the BODMAS rule, the priority of order should be followed.

Note: Addition and subtraction can be treated on the same priority (from left to right) when they are in consecutive order.

√483.9915 + (7.0215)² = ? * 6.0212  – 1.0215³
Approximating the value to the nearest integer:
√484+7² =?*6.0212-1³
22+49=?×6-1
71+1=6?
72=6?
?=
?=12

EXAMPLE 5: 64% of (?) + (?)% of 76 = 76.89% of 286 + 73.87% of 147

This is written as:
⇒   (Cancel 100s)
⇒ 64 (?) + (?)76 = 77 × 286 + 74 × 147 
⇒ 140(?) = 22022 + 10878 
⇒ 140(?) = 32900 
⇒ (?) =  
Hence, (?) = 235

EXAMPLE 6: (√80.997 – √25.001) × (√120.98 + √16.02) = ?

Approximating the values: 
(√81 – √25) × (√121 + √16) = ? 
(9 – 5) × (11 + 4) = ? 
4 × 15 = ? 
? = 60

You can check other quantitative Aptitude study materials here:

S.No	Topics
1	Simplification & Approximation
2	Calculation Short Tricks
3	D.I Basics
4	Number series
5	Quadratic Equation
6	Simple Interest
7	Compound Interest
8	Mixture & Alligation
9	Partnerships
10	Percentages
11	Pipes & Cisterns
12	Age-based problems
13	Profit, Loss & Discount
14	Ratio & Proportion
15	Time, Speed & Distance
16	Time & Work
17	Probability

EXAMPLE 7: (14.99% of 4799.995)  ? = (170% of 7.111)^{2   2} 
 ?  
 ? 5  

EXAMPLE 8: (89)² + ? % of 560.30 + (14.99)²= 95.45*286   (89)² + ? % of 560.30 + (14.99)²= 95.45*286 
7921 + 560x/100 + 225= 27170 
560x/100= 27170- 7921-225 
560x/100= 19024 
x= 3397  

EXAMPLE 9: 100/3 % of 768.9 + 25% of 161.2 – 68.12=?   100/3 % of 768.9 + 25% of 161.2 – 68.12=? 
= 100/3 * 1/100 *768 + 40 – 68 
= 256+ 40 -68 
= 228  

EXAMPLE 10: 795.002÷14.998+768.025÷11.985-1273.025÷19.022=x   x=795÷15+768÷12-1273÷19 
x=53+64-67 
x=50    

Attempt Important Quizzes of Quantitative aptitude: Quantitative Aptitude Quiz