Simplifications For Beginners

Simplifications Plays an Important Role in Banking Exams and Other Competitive Exams Now days.
As we know Simplification problems any can do it. but we have to Do Correctly within the time limits. By shortcuts Method. That's Important.

Simplification

We must learn to do the basic calculations faster. It saves few seconds from each question. And at the end, we find that at least 5-10 minutes have been saved.

What to do for faster basic calculation:
1. Remember the tables upto 30.
2. Learn the method of multiplication.
3. Learn the method of addition - subtraction in a single line or column.
4. Learn the method of approximation.
5. Learn to compare two fractions.
6. Remember square roots, squares, cubes and cube roots. (Shortcuts)
7. Remember fractional value of percentage.
8. Remember decimal values of reciprocals.
9. Do calculations mentally. Don’t write unnecessary steps in Exams.
10. Learn the laws of surds and indices.
11. VBODMAS Rule:
V stands for Vinculum or bar
B Stands for brackets and operation of brackets in
the order (), {}, []
O stands for “of”
D stands for division (÷)
M stands for multiplication (×)
A stands for addition (+)
S stands for substraction (-)
12. Some algebraic formulae:
1. (a + b)2 = a2 + b2 + 2ab
2. (a – b)2 = a2 + b2 – 2ab
3. (a + b)2 + (a – b)2 = 2(a2 + b2)
4. (a + b)2 – (a – b)2=4ab
5. (a + b) (a – b) = a2 – b2
6. (a + b)3 = a3 + 3a2b + 3ab2 + b3
7. (a – b)3 = a3 – 3a2b + 3ab2 – b3
8. a3 + b3 = (a + b) (a2 – ab + b2 )
9. a3 – b3 = (a – b) (a2 + ab + b2)

For More Practice Problems Stay in Touch

Simplification Practice Set Complete

Basic Calculations 

Download Here

Free Online Tests (Banking)

Click Here for Free IBPS Banking Exams

Approximation (5 marks) RBI/IBPS

1. 816.23/34.98 × 24.999 = ?

1.560

2.540

3.520

4.580

5.600

2.(4722+3272+5324)/(491+769+132)=?

1.40

2.10

3.15

4.25

5.20

3.22 1/3 % of 435.1 -  11/7 % of 1734.68 = ?

1.59

2.62

3.50

4.69

5.78

4.(1681)^1/2 + (4094)^1/3 = ?

1.57

2.75

3.78

4.67

5.76

5.(803.63)² = ?

1.506000

2.787800

3.646400

4.767600

5.566000

6.(1.2)² / 1.3333  = (1.1)^? / (1.22)³

1.8

2.6

3.7

4.5

5.3

7. 2809/27.86 × 6.26 - 125.88 - 246.18 = ?

1.245

2.266

3.254

4.238

5.272

8.(13.67)² - (4.77)²+ (8.26)³ - (5.23)³ = ?

1.636

2.600

3.520

4.624

5.612

9.21% of 234.20 + 54% of 150 - 3.76% of 102.05 = ?

1.129

2.122

3.147

4.136

5.167

10.(1218)^2 / 18 = ? × 1224

1.90

2.67

3.70

4.60

5.78

Directions: What approximate value will come in place of question mark (?) in
the following questions (You are not expected to calculate the exact value).
11. 9228.789 – 5021.832 + 1496.989 = ?
a) 6500 b) 6000 c) 6300 d) 5700 e) 5100

12. 1002 ÷ 49 × 99 – 1299 = ?
a) 700 b) 600 c) 900 d) 250 e) 400

13. 29.8% of 260 + 60.01% of 510 – 103.57 = ?
a) 450 b) 320 c) 210 d) 280 e) 350

14. (21.98)2 – (25.02)2 + (13.03)2 = ?
a) 25 b) 120 c) 10 d) 65 e) 140

Speed Test - 02 (Digital Root Method)

Speed Test Based On Digital Root + Unit Digit Method

(you can solve 15 questions in less than 5 - 7 minutes)

1. 135% of 342 - 342% of 13.5 = ?
(1) 411.13 (2) 412.23 (3) 413.33 (4) 414.43 (5) 415.53

2. Sqroot 13.3225 = ?
(1) 3.45 (2) 3.55 (3) 3.65 (4) 3.75 (5) 3.85

3. 144 × 7 + 612 × 4 = ?% of 12800
(1) 24 (2) 27 (3) 30 (4) 32 (5) 35

4. 1859 /? = ? / 275
(1) 715 (2) 725 (3) 745 (4) 775 (5) 825

5. . 36% of 17/123  of 18 / 41 of 25215 = ?
(1) 542.2 (2) 544.6 (3) 546.5 (4) 547.4 (5) 550.8

6. 76% of 960 - 45% of 148 = ?% of 5525
(1) 15 (2) 20 (3) 24 (4) 12 (5) None of these

7. 23/7 of 49/11 of 3/35 of 3080 = ?
(1) 3864 (2) 3948 (3) 4014 (4) 4124 (5) None of these

8. 4/7 of 3/11 of 24/13 of 15015 = ?
(1) 4280 (2) 4320 (3) 4480 (4) 4550 (5) None of these

9. 984 + 3.75 × 440 - 1.25 × 248 = ?
(1) 2148 (2) 2264 (3) 2324 (4) 2420 (5) None of these

10. 18.5 % of 7200 + 27.8% of 1800 + 16.6 = (?)2
(1) 37 (2) 39 (3) 43 (4) 47 (5) None of these

11. 924 × 0.75 + 848 × l.25 = ? × 0.25
(1) 7004 (2) 7008 (3) 7012 (4) 7016 (5) 7020

12. 17/7 of 3/8 of 5/4 of ? = 4590
(1) 3612 (2) 4032 (3) 4448 (4) 4804 (5) None of these

13. 13% of 1335 + ?% of 1135 = 366.5
(1) 11 (2) 13 (3) 15 (4) 17 (5) 19

14. 11/113 of 7/85 of 115260 = ?
1) 832 (2) 848 (3) 886 (4) 904 (5) None of these

15. 2786 + 105 × ? = 304 × 14
(1) 12 (2) 14 (3) 16 (4) 18 (5) 22

Simplification Practice Set -01 (Digital Root Method)

This Section Contains, Total 15 Questions, and 10 Minutes, You can Solve By Normal BODMAS rule.


Q(1 –10) what should come in place of question mark (?) in the following questions: –
1.   1777 – 2349 – 1345 + 6523 = ?
 A) 4706    B) 4606        C) 4976      D) 4176        E) 5276  (Digital Root Method)

Lets solve by DR Method (Digital Root)
Let (1+7+7+7) - (2+3+4+9) - (1+3+4+5) + (6+5+2+3) = x
    now (22) - (18) - (13) + (16) = x
    now again Digital Root to Single Root    
        4 - 9 - 4 + 7 = x
       so, 9+7 = x ( U can see, There is no value for 9 in digital root)
                   7 = x  (Digital Root of above Equation is 7)
Now  Check the Options
A) 4+7+0+6 = 17 = 8 (not match)
B) 4+6+0+6 = 16 = 7 (Match with digital root of x)
C) 3+9+7+6 = 17 = 8 (Not match)
D) 5+2+7+6 = 20 = 2 (Not Match)
So, B) is the right Answer

Similarly You can solve Below Problems

 3.  2387 – 123 + 980 = ? – 145 + 945
A) 2244              B) 2434         C) 2444        D) 2354        E) 2544                    (Digital Root Method)
2+3+8+7    -     1+2+3      + 9+8+0   =  ?   - 1+4+5         +     9+4+5
2 -  6 +8 =  ? - 1 + 9
4 = ? +8
4 -8  = ?
-4 = ?
(If your final Digital is in Negative Add "9'' to it to make it positive)
So, 9-4 = ?
5 = ?

Now Find out the Digital Root of All the Options, if any option whose digital root is exactly "7" that is the Answer

A) 2+2+4+4 = 12 = 3 
B) 2+4+3+4 = 13 = 4
C) 2+4+4+4 = 14 = 5 (Match) Exactly
D) 2+5+4+4 = 15 = 6 



4.   1.96*1.96 + 1.04*1.04 – 2.08*1.96 = ?
      A) 0.7464      B) 0.8464     C) 0.9464     D) 0.8262      E) none of these (Digital Root Method)

Now Lets Do it Without Pen / Paper 
the Digital Root of Above Equation is as follows
(Note : Wherever the "9" comes in Digital Root just neglect it) 
Now,  7*7 + 5*5 - 1*7 =  49 + 25 - 7 = 4 + 7 - 7 = X, now final Digital Root x = 4
Match with Options 
(neglect the Decimal Points)
A) 7+4+6+4 = 21 = 3 (Not Match)
B) 8+4+6+4 = 22 = 4 (Match)
C) 9+4+6+4 = 23 = 5 (Not Match)
D) 8+2+6+2 = 18 = 9 (not Match)
So, B) is the Right Choice

5.   41% of 801 – 150.17 = ? – 57% of 910 (Approximation method)
         A) 693 B) 694 C) 697 D) 707 E) none of these
You Can't Apply Digital Root For Approximations, you can do it by Normal Method


7. 5016 x 1001 - 333x77+22 = ? x 11 (Digital Root Method)
       a. 435570           b. 454127           c, 527240          d. 366531        e. 511990
Now according to Digital Root Method 
The Digital Root of above Equation is
6 - 9 + 4 = x * 2
1 = x * 2  (Just Neglect 9)
Now we have to Make LHS = RHS, by suitable "x'' value putting from 1 to 9)
So, If we Substitute X = 5  
We get 1  = 5 * 2
   1  =  10
1  =  1
SO, Clearly the Digital Root of above Equation is 5 (as X = 5)
Now Find out the digital root of given options
A) 4+3+5+5+7+0 = 24 = 6
B) 4+5+4+1+2+7 = 5  (Match)
C) 5+2+7+2+4+0 = 20 = 2 
D) 3+6+6+5+3+1 = 6
E) 5+1+1+9+9+0 = 7


8. (31% of 260) x ? = 12896                                      (Digital Root Method)
a. 150          b. 140          c. 160          d. 180        e. 170


9. 416 x ? x 8 = 59904                           (Digital Root Method)
 a. 17           b. 12           c. 21          d. 15          e. 18

10. 12.8% of 8800 - 16.4% of 5550 = 20% of ?                              (Digital Root Method)
a. 964             b. 996              c. 1004           d. 1081             e. 1124

11. 14 x 18.6 /12 + 19.3  = ?                                      
a. 41           b. 33.5          c. 291.9             d. 8.32        e. 65.50

12. 53% of 120 + 25% of 862 = ?% of 500                          (Digital Root Method)
a. 42.50           b. 55.82          c.  63.68          d. 38.89         e. 82.65

13. 2567 / 17  x 3 =  ? + 180                              (Digital Root Method)
a. 51             b. 271             c. 273          d. 73           e. 141

14. 7.5% of 140 + 2.5% of 80 = ?                             (Digital Root Method)
a. 125          b. 18.5           c. 145          d. 14.5           e. 12.5

15. 135% of 342 - 342% of 13.5 = ?                             (Digital Root Method)
a. 411.13         b. 412.23       c. 413.33       d. 414.43         e. 415.53