# Simplification Questions for Bank Exam with Solution

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Here, I’m going to explain the most important simplification questions for bank exam with complete solution.

Now, it doesn’t mean that these questions are useful for only bank exams. You can also practice all these questions for any of the competitive exams.

Simplification is a very important chapter from the perspective of competitive exams.

Each competitive exam asks at least two questions of this chapter, so you must prepare for this.

Without wasting your valuable time let’s start the topic that is about simplification questions for bank exam.

## Basic formulas –

1. ( a + b )² = a²+b²+2ab

2. ( a – b )² = a²+b²-2ab

3. ( a + b )² = ( a – b )²+4ab

4. ( a – b )² = ( a + b )²-4ab

5. ( a²-b² ) = ( a + b ) ( a – b )

6. ( a + b )³ = a³+b³+3ab ( a + b )

7. ( a – b )³ = a³-b³-3ab ( a – b )

8. ( a³ – b³ ) = ( a – b ) ( a²+b²+ab )

9. ( a³ + b³ ) = ( a + b ) ( a²+b²-ab )

10. ( a + 1/a )² = a²+1/a²+2

11. ( a – 1/a )² = a²+1/a²-2

12. ( a – 1/a )² = ( a + 1/a )² – 4

13. ( a + 1/a )² = ( a – 1/a )² + 4

14. ( a – 1/a )³ = a³-1/a³-3(a-1/a)

15. ( a + 1/a )³ = a³+1/a³+3(a+1/a)

16. ( a + b + c ) ² = a²+b²+c²+2ab+2bc+2ca = a²+b²+c²+2( ab + bc + ca )

17. a³+b³+c³-3abc = ( a + b + c ) ( a²+b²+c²-ab-bc-ca ) = 1/2×(a + b + c ) [ ( a – b )²+( b – c )²+( c-a )² ]

18. If a+b+c =0, then a³+b³+c³-3abc = 0

19. BODMAS rule It stands for Bracket, Of, Division, Multiplication, Addition and Subtraction.

It’s mandatory to solve simplification questions in BODMAS order.

## Simplification Questions for Bank Exam with Solution –

Here are 21 the most important simplification questions for bank exam, so that you can practice valuable questions.

All these questions are related to previous years.

### Q1. Find the value of 15.2+5.8÷2.9×2-3.5×2÷0.5.

( a ) 4.9

( b ) 5.2

( c ) 3.7

( d ) 5.6

#### Solution –

15.2+5.8÷2.9×2-3.5×2÷0.5

=15.2+2×2-3.5×4

=15.2+4-14

=5.2 ( Ans )

### Q2. What is the value of 2.8+(5.2÷1.3×2)-6×3÷8+2 ?

( a ) 10.55

( b ) 8.96

( c ) 9.35

( d ) 10.75

#### Solution –

2.8+(5.2÷1.3×2)-6×3÷8+2

=2.8+(4×2)-18/8+2

=2.8+8-2.25+2

=10.55 ( Ans )

### Q3. Find the value of 2×3÷6×2÷(4+4×4÷16-4).

( a ) 3

( b ) 4

( c ) 2

( d ) 5

#### Solution –

2×3÷6×2÷(4+4×4÷16-4)

=2×1/2×2÷(4+4×1/4-4)

=2÷(4+1-4)

=2÷(5-4)

=2÷(1)

=2 ( Ans )

### Q4. Find the forth root of 24010000.

( a ) 60

( b ) 80

( c ) 90

( d ) 70

#### Solution –

24010000 ( given )

Square root

√24010000

=√2401×√10000

=49×100

=4900

Again square root

√4900

=√49×√100

=7×10

=70 ( Ans )

### Q5. What will be the value of (3.25×3.20-3.20×3.05)÷0.064 ?

( a ) 10

( b ) 1/10

( c ) 5

( d ) 10.2

#### Solution –

(3.25×3.20-3.20×3.05)÷0.064

=(10.4-9.76)÷0.064

=0.64÷0.064

=10 ( Ans )

### Q6. If 4x²=15²-9², find the value of x.

( a ) 9

( b ) 6

( c ) 12

( d ) 4

#### Solution –

4x²=15²-9² ( given )

4x²=(15+9)(15-9)

4x²=24×6

4x²=144

x²=144/4

x²=36

x=√36

x=6 ( Ans )

### Q7. If 2x-5y=5 and 2x-y=9, find the value of x-y.

( a ) 1

( b ) 2

( c ) 3

( d ) 4

#### Solution –

2x-5y=5…….(1)

2x-y=9……..(2)

Solving the equations

2x-5y-2x+y=5-9

-5y+y=-4

-4y=-4

y=1

Put the value of y in equation (1)

2x-5×1=5

2x-5=5

2x=10

x=5

Now, x-y=5-1=4

x=4 ( Ans )

( a ) 24

( b ) -24

( c ) 30

( d ) -32

∛-13824

=∛-24×-24×-24

=-24 ( Ans )

### Q9. If √x÷√441=0.02, find the value of x.

( a ) 1.764

( b ) 17.64

( c ) 0.1764

( d ) 176.4

#### Solution –

√x÷√441=0.02 ( given )

⇒√x/21=0.02

⇒√x/21=2/100

⇒√x=42/100

Squaring both sides

⇒x=(42)²/(100)²

⇒x=0.1764 ( Ans )

### Q10. Find the value of \frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}.

( a ) 6/30

( b ) 5/12

( c ) 5/39

( d ) 6/39

#### Solution –

\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}

=\frac{1}{3×5}+\frac{1}{5×7}+\frac{1}{7×9}+\frac{1}{9×11}+\frac{1}{11×13}

=\frac{1}{2}[\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}]

=\frac{1}{2}[\frac{1}{3}-\frac{1}{13}]

=\frac{1}{2}×\frac{10}{39}

=5/39 ( Ans )

### Q11. The value of 2√54-6\sqrt{2/3}-√96 is

( a ) 0

( b ) 1

( c ) 3

( d ) 5

#### Solution –

2√54-6\sqrt{2/3}-√96

=2\sqrt{9×6}-2×3\sqrt{2/3}\sqrt{16×6}

=6\sqrt{6}-2\sqrt{\frac{2}{3}×9}-4\sqrt{6}

=6\sqrt{6}-2\sqrt{6}-4\sqrt{6}

=0 ( Ans )

### Q12. 0.4\bar{7}+0.5\bar{03}-0.3\bar{9}×0.\bar{8}is equal to

( a ) 0.3\bar{65}

( b ) 0.4\bar{35}

( c ) 0.4\bar{65}

( d ) 0.6\bar{25}

#### Solution –

0.4\bar{7}+0.5\bar{03}-0.3\bar{9}×0.\bar{8}

=\frac{47-4}{90}+\frac{503-5}{990}-\frac{39-3}{90}×\frac{8}{9}

=\frac{43}{90}+\frac{498}{990}-\frac{36}{90}×\frac{8}{9}

=\frac{43}{90}-\frac{32}{90}+\frac{498}{990}

=\frac{11}{90}+\frac{498}{990}

=\frac{121+498}{990}

=\frac{619}{990}

=0.6\bar{25}

### Q13. \frac{(0.96)³-(0.1)³}{(0.96)²+0.096+(0.1)²} is equal to

( a ) 0.98

( b ) 0.86

( c ) 0.45

( d ) 0.69

#### Solution –

\frac{(0.96)³-(0.1)³}{(0.96)²+0.096+(0.1)²}

=\frac{(0.96-0.1)(0.96)²+0.96×0.1+(0.1)²}{(0.96)²+0.96×0.1+(0.1)²}

=0.96-0.1

=0.86 ( Ans )

### Q14. (100)^{\frac{1}{2}}×(0.001)^{\frac{1}{3}}-(0.0016)^{\frac{1}{4}}×(3)^{0}+(\frac{5}{4})^{-1}, find the value.

( a ) 2.5

( b ) 1.6

( c ) 1.9

( d ) 2.8

#### Solution –

(100)^{\frac{1}{2}}×(0.001)^{\frac{1}{3}}-(0.0016)^{\frac{1}{4}}×(3)^{0}+(\frac{5}{4})^{-1}

=(10)^{2×\frac{1}{2}}×(0.1)^{3×\frac{1}{3}}-(0.2)^{4×\frac{1}{4}}×1+4/5

=10×0.1-0.2+4/5

=1-2/10+4/5

=1-1/5+4/5

=\frac{5-1+4}{5}

=\frac{8}{5}

=1.6 ( Ans )

### 15. 111\tfrac{1}{2}+111\tfrac{1}{6}+111\tfrac{1}{12}+111\tfrac{1}{20}+111\tfrac{1}{30} is equal to

( a ) 555\tfrac{6}{5}

( b ) 111\tfrac{2}{9}

( c ) 555\tfrac{5}{6}

( d ) 111\tfrac{1}{3}

#### Solution –

111\tfrac{1}{2}+111\tfrac{1}{6}+111\tfrac{1}{12}+111\tfrac{1}{20}+111\tfrac{1}{30}

=5×111+\frac{30+10+5+3+2}{60}

=5×111+\frac{50}{60}

=555+\frac{5}{6}

=555\tfrac{5}{6} ( Ans )

### Q16. What will be the value of 48÷12×[\frac{9}{8}of\frac{4}{3}÷\frac{3}{4}of\frac{2}{3}] ?

( a ) 13

( b ) 18

( c ) 12

( d ) 16

#### Solution –

48÷12×[\frac{9}{8}of\frac{4}{3}÷\frac{3}{4}of\frac{2}{3}]

=4×[(\frac{9}{8}×\frac{4}{3})÷(\frac{3}{4}×\frac{2}{3})]

=4×[\frac{3}{2}÷\frac{1}{2}]

=4×\frac{3}{2}×\frac{2}{1}

=12 ( Ans )

### Q17. If M=\frac{3}{7}×\frac{5}{6}×\frac{2}{3}+\frac{1}{5}×\frac{3}{2} and N=\frac{2}{5}×\frac{5}{6} × 3 + \frac{3}{5}×\frac{2}{3}×\frac{5}{3}, find the value of M/N.

( a ) 305/113

( b ) 113/305

( c ) 113/350

( d ) 131/302

#### Solution –

M=\frac{3}{7}×\frac{5}{6}×\frac{2}{3}+\frac{1}{5}×\frac{3}{2} ( given )

=\frac{5}{21}+\frac{3}{10}

=\frac{50+63}{210}

M=113/210

N=\frac{2}{5}×\frac{5}{6} × 3 + \frac{3}{5}×\frac{2}{3}×\frac{5}{3} ( given )

=1+\frac{2}{3}

N=5/3

Now,

M/N=113×3/210×5

M/N=113/350 ( Ans )

### Q18. What will be the value of K in the equation 2.5+0.5-[1.6-{3.2-(3.2+2.1)÷K}]=0.65 ?

( a ) 3.5

( b ) 2.9

( c ) 1.34

( d ) 7

#### Solution –

2.5+0.5-[1.6-{3.2-(3.2+2.1)÷K}]=0.65

3.0-[1.6-{3.2-(5.3÷K)=0.65

3.0-[1.6-3.2+(5.3÷K)=0.65

3.0-1.6+3.2-(5.3÷K)=0.65

4.6-(5.3÷K)=0.65

4.6-0.65=(5.3÷K)

3.95=(5.3÷K)

3.95=5.3/K

K=5.3/3.95

K=1.34 ( Ans )

### 19. \frac{4-\sqrt{0.04}}{4+\sqrt{0.4}} is equal to

( a ) 2.36

( b ) 6.25

( c ) 1.01

( d ) 0.82

#### Solution –

\frac{4-\sqrt{0.04}}{4+\sqrt{0.4}}

=\frac{4-\sqrt{4/100}}{4+\sqrt{4/10}}

=\frac{4-\sqrt{4/100}}{4+\sqrt{4/10}}

=\frac{4-0.2}{4+0.632}

=\frac{3.8}{4.632}

=0.82 ( Ans )

### 20. Find the value of \frac{\sqrt{2}-1}{\sqrt{2}+1} if √2=1.414.

( a ) 0.172

( b ) 0.568

( c ) 0.432

( d ) 0.156

#### Solution –

\frac{\sqrt{2}-1}{\sqrt{2}+1}

Rationalizing it

=\frac{\sqrt{2}-1}{\sqrt{2}+1}×\frac{\sqrt{2}-1}{\sqrt{2}-1}

=\frac{2+1-2\sqrt{2}}{1}

=3-2×1.414

=3-2.828

=0.172 ( Ans )

### 21. Find the value of x in the equation \frac{50}{x}=\frac{x}{12\tfrac{1}{2}}.

( a ) 49

( b ) 25

( c ) 64

( d ) 81

#### Solution –

\frac{50}{x}=\frac{x}{12\tfrac{1}{2}}

\frac{50}{x}=\frac{x}{25/2}

\frac{50}{x}=\frac{2x}{25}

50×25=2x²

x²=625

x=25 ( Ans )

## Questions for practice –

1. Find the value of 3.8+(8.2÷4.1×2)-4×3÷1.2.

2. Find the value of (5+3÷5×5)÷(3÷3 of 6) of (4×4÷4 of 4+4÷4).

3. 2.8+(5.2÷1.3×2)-6×3÷8+2 is equal to

4. Simplify the equation (x+4)²+(x-2)².

5. What will be the value of x in the equation 0.\bar{3}+0.\bar{6}+0.\bar{7}+0.\bar{8}=x?

1. (-2.2)
2. 48/5
3. 10.55
4. (2x²+4x+20)
5. 8/3

Final words –

I hope that you’ve found here important simplification questions for bank exam.