Explore topic-wise InterviewSolutions in .

• Can receive service with the help of information technology. 
• Government services offered speedily and with less expense. 
• Efficiency of the offices and quality of the service get enhanced. 

Functions of the Back office: 

The functions carried out by the Back office are:

1. Sending statements to clients on mail and at the addresses provided if required. 

2. Resolving clients‟ queries 

3. Processing clients‟ standing instructions 

4. Checking and Opening Clients‟ accounts as per the details provided. 

5. Issuance of cheque books to clients 

6. Cheque clearing 

7. Positioning for all Bank products viz. cheques, cards, personal loan, mortgage loan etc.

(c) The series is as follows: ÷ 5
Hence, ? = 2800 ÷ 5 = 560

(c) The given number series is based on the following pattern:
22 + 1² = 22 + 1 = 23
23 + 2² = 23 + 4 = 27
27 + 3² = 27 + 9 = 36
36 + 4² = 36 + 16 = 52
52 + 5² = 52 + 25 = 77
? = 77 + 62
= 77 + 36 = 113

Calculation:

7 + 2² = 11

11 + 3² = 20

20 + 4² = 36

36 + 5² = 61

61 + 6² = 97

∴ The missing number is 61.

Calculation:

The series follows following pattern:

⇒ 4 × 3 = 12

⇒ 12 × 3 = 36

⇒ 36 × 3 = 108

⇒ 108 × 3 = 324

⇒ 324 × 3 = 972

∴ The value of ? is 108

(c) 7 = 23 – 1
26 = 33 – 1
63 = 43 – 1
124 = 53 – 1
215 = 63 – 1
? = 73 – 1 = 342

The teaching and learning of mathematics have always been a major concern in education. The National Policy of Education (1986) lays down the importance of "mathematics" as a vehicle for developing creativity.

• The teacher should use effective teaching methods of mathematics so that individualized discovery-oriented (or problem-solving) learning could be fostered.

Hence, ‘‘Mathematics is the language in which God has written the universe.’’ is quoted by Galileo.

Mathematics is the study of geometrical figures, their co-relation, and their dependency on each other. It deals with quantity, measurement, and spatial relationships.

• The National Policy of Education (1986) lays down the importance of "mathematics" as a vehicle for developing creativity.
• The teacher should use effective teaching methods of mathematics so that individualized discovery-oriented (or problem-solving) learning is fostered.

Hence, it could be concluded that "things are numbers" is quoted by Pythagoras.

Series pattern Given series

7 7

⇒ 7 + (1)³ 8

⇒ 8 - (2)³ 0

⇒ 0 + (1)³ 1

⇒ 1 - (2)³ - 7

Mathematics is the study of numbers, shapes, quantities, and patterns. Mathematics is the ‘queen of all sciences and its presence is there in all the subjects. It acts as the basis and structure of other subjects.

According to Bacon, ‘‘Mathematics is the gateway and key to all sciences.’’ 

Science and mathematics

• Perhaps mathematics and science share the closest relationship. There is no branch of science that does not use mathematics
• Science and mathematics are closely related and thus we say science is incomplete without mathematics.
• Most of the concepts have evolved from experimentation or observation but have been established as scientific theories by the use of mathematical interpretations
• In every branch of science, mathematics occur in one way or the other in the form of numerals, symbols, formula, computations, etc.  For example in physics, the topics like gravitation, motion, energy, and power, heat and thermodynamics, waves and oscillations, electricity, magnetism, electric current, optics, etc. employ mathematical symbols and calculations.
• In chemistry, the structure of atoms, the laws of chemical combination, elements, and compounds make use of mathematics equations, combinations, and proportions.
• In biology and life sciences a large number topic uses the principles of mathematics. For example, the arrangement of human body structure, measurement of blood pressure, and temperature involve mathematics. It is difficult to enlist all the areas of science where mathematical knowledge is required to understand the concepts.
• In fact, there is hardly any area in all branches of science where mathematics is not needed.

Hence, we can conclude that the above statement is quoted by Bacon

If the class mid points in a frequency distribution of a group of persons are: 125, 132, 139, 146, 153, 160, 167, 174, 181 pounds, then the size of the class is 7. 

Series pattern. Given series

8 8

8 + 11= 19

19 + 11 =  30

30 + 11 = 41

41 + 11 =  52

52 + 11 = 63 

The series follows the following pattern:

132 + 7 = 139

139 + 14 = 153

153 + 21 = 174

174 + 28 = 202

202 + 35 = 237

237 + 42 = 279

∴ The missing term in the series is 237.

Calculation:

The series follows the following pattern.

⇒ (19 - 3) × 6 = 96

⇒ (96 - 19) × 5 = 385

⇒ (385 - 96) × 4 = 1156

⇒ (1156 - 385) × 3 = 2313

Calculation: 

6 + 9 = 15

9 + 15 = 24

15 + 24 = 39

24 + 39 = 63

The Correct option is 1 i.e. 39

Considering the given series

14, 28, 56, 98, 196, 266

The logic of the given series can be explained as

14 + 14 × 1 = 28

28 + 14 × 2 = 56

56 + 14 × 3 = 98

98 + 14 × 5 = 168

168 + 14 × 7 = 266

∴ Wrong term in given number series is 196.

Given:

The number series:

0.5, 1.5, 5, ?, 76, 385

Concept Used:

Number series following a fixed pattern.

Calculation;

The given number series follows the pattern:

0.5 × 1 + 1 = 1.5

1.5 × 2 + 2 = 5

5 × 3 + 3 = 18

18 × 4 + 4 = 76

76 × 5 + 5 = 385

∴ The number coming in place of “?” in the given number series is 18

Calculation∶

The series follows following pattern

9 × 1 + 2 = 11

10 × 2 + 3 = 23

11 × 3 + 4 = 37

12 × 4 + 5 = 53

13 × 5 + 6 = 71

14 × 6 + 7 = 91

Series pattern Given series

3 3

3 × 4 - 2 =10

10 × 4 + 1 = 41

41 × 4 - 2 =162

162 × 4 + 1 = 649

The series follows the following pattern:

10 × 1 + 1 = 11

11 × 2 + 2 = 24

24 × 3 + 3 = 75

75 × 4 + 4 = 304

304 × 5 + 5 = 1525

Considering the given series

24, 8, 12, 18, 36, 90

The logic of the given series can be explained as

24 × 0.5 = 12

12 × 1 = 12

12 × 1.5 = 18

18 × 2 = 36

36 × 2.5 = 90

∴ Wrong term in given number series is 8.

GIVEN :

Pipe A alone can empty the tank in 12 hours

Pipe B alone can fill the tank in 24 hours and pipe C alone can fill the tank in 16 hours

CONCEPT :

Pipe & Cistern (Negative work)

CALCULATION :

Pipe A's 1 hour's work = 1/12

Pipe B's 1 hour's work = 1/24

Pipe C's 1 hour's work = 1/16

Pipe (A + B + C)'s 1 hours work = 1/24 + 1/16 - 1/12 = 1/48

∴ In 48 hours tank will be completely filled.

Calculation:

The given number series follows this pattern:

2 + 4 = 6

6 + 5 = 11

11 + 6 = 17

17 + 7 = 24

24 + 8 = 32

32 + 9 = 41

∴ The wrong number in the given number series is 12

Calculation∶

The series follows following pattern

1 × 3 + 2 = 5

3 × 5 + 4 = 19

5 × 7 + 6 = 41

7 × 9 + 8 = 71

9 × 11 + 10 = 109

Concept used:

The series follows following pattern

Calculation:

22 + 3² = 31

76 + 5² = 101

31 + 3² = 40

101 + 5² = 126

∴ The next number in the series will be 40

Calculation:

The series follows the following pattern

6

6 × 0.5 = 3

3 × 1 = 3

3 × 2 = 6

6 × 4 = 24

24 × 8 = 192

∴ The wrong number in the series is 4.5.

The pattern of given series can be explained as:

4 + 10 = 14

14 + 20 = 34

34 + 40 = 74 ≠ 66

74 + 80 = 154

∴ The wrong term is 66.

Calculation:

The series follows following pattern

⇒ 39 + 2 = 41

⇒ 41 + 2 = 43

⇒ 43 + 2 = 45

⇒ 45 + 2 = 47

∴ The required answer is 47

Considering the given series

5, 23, 43, 66, 94, 131

The logic of the given series can be explained as

∴ Wrong term in given number series is 131.

Calculation:

The given number series follows this pattern:

3 + 2⁰ = 4

4 + 2¹ = 6

6 + 2² = 10

10 + 2³ = 18

18 + 2⁴ = 34

34 + 2⁵ = 66

∴ The wrong number in the given series is 11

Given:

288, 359, 440, 525, 620, 723

Calculation:

⇒ (17² - 1) = 288

⇒ (192 - 2) = 359

⇒ (212 - 3) = 438

⇒ (232 - 4) = 525

⇒ (252 - 5) = 620

⇒ (272 - 6) = 723

∴ The wrong term is 440.

Speed of train = 132 *(5/18) m/sec = 110/3 m/sec. 

Distance covered in passing the platform = (110 + 165) m = 275 m. 

Time taken =275 *(3/110) sec =15/2 sec = 7 1/2 sec

Speed of the train = (30 x 5/18) m / sec = (25/3) m/ sec. 

Distance moved in passing the standing man = 100 m. 

Required time taken = 100/(25/3) = (100 *(3/25)) sec = 12 sec

Relative speed of the trains = (42 + 48) kmph = 90 kmph 

=(90*5/18) m / sec = 25 m /sec. 

Time taken by the trains to'pass each other = Time taken to cover (137 + 163) m at 25 m /sec =(300/25) sec = 12 sec

Given:

Given series is 

34  17  17  34  ?

 1/2 , 1 , 2 , 4 , 8 , 16

Since it is started from 1/2 we are multiplying each term, so 3 will not come as multiplying factor.

Calculation:

First step 

⇒ 34 × 0.5

⇒ 17

Second step

⇒ 17 × 1

⇒ 17

Third step

⇒ 17 × 2

⇒ 34

So on, 

Fourth step 

⇒ 34 × 4

⇒ 136

∴ The required missing number is 136.

Calculation∶

The series follows following pattern

21 + 13 = 34

34 + 21 = 55

55 + 34 = 89

89 + 55 = 144

144 + 89 = 233

GIVEN:

Loss = 20% when SP = Rs. 2000

FORMULA USED:

Profit = [(SP - CP)/CP] × 100

Loss = [(CP - SP)/CP] × 100

CALCULATION:

Since loss is of 20% we can calculate CP as:

20 = [(CP - 2000)/CP] × 100

⇒ CP = 2000/0.8 = 2500

Now he sells the pen at Rs. 2250:

So,

Loss % = [(2500 - 2250)/2500] × 100

= 25000/2500

Loss % = 10% 

GIVEN:

A person sells his watch at a cost of Rs. 2250 and thus incurs a loss. If he has to sell his watch at Rs. 2000 and his loss % increases by 10%.

CONCEPT:
Basic concept of Profit and Loss.

FORMULA USED:

SP = CP × [1 – Loss/100]

CALCULATION:

When selling the watch for Rs. 250 less he incurs an extra loss of 10% then we can say that

10% of CP = 250

⇒ CP = Rs. 2500

GIVEN:

In a certain store, the profit is 210% of the cost.

CONCEPT:
Basic concept of Profit and Loss.

FORMULA USED:

Profit on the selling price = [(SP – CP)/SP] × 100

CALCULATION:

Let Cost price = Rs. 100

Then, Profit = Rs. 210,

So,

Selling price = Rs. 310

New CP = 140% of Rs. 100 = Rs. 140

New SP = Rs. 310

Hence,

Profit = Rs. (310 – 140) = Rs. 170

Given 

The profit percentage = 320% of CP

Formula Used 

Profit% = (Profit/CP) × 100

Calculation

Let the cost price be 100x 

so, Profit = 320% of 100x = 320x

then, selling price = 420x

Now, cost price increased by 25% 

New, Cost price = 125x 

New Profit = 420x - 125x = 295x 

Profit percent on selling price = (295x/420x) × 100 = 70% 

∴ The required percentage is 70% 

Length of the rectangular garden = 40 m 

Area of the rectangular garden = 1000 sq. m. 

∴ length × breadth = 1000 

∴ 40 × breadth = 1000

∴ breadth = 1000/40

= 25 m

Now, perimeter of the rectangular garden = 2 × (length + breadth)

= 2 (40 + 25) 

= 2 × 65 

= 130 m

Length of one round of fence = circumference of garden – width of the entrance

= 130 – 4 

= 126 m

∴ Total length of fencing = length of one round of wire × number of rounds = 126 × 3

= 378 m

∴ Total cost of fencing = Total length of fencing × cost per metre of fencing

= 378 × 250 

= 94500 

∴ The cost of fencing the garden is Rs 94500.

Given:

Discount on labeled price = 10%

Labeled price of yarn = Rs. 3500

Profit on selling price = Rs. 250

Formula used:

Discount = Labeled price × (100 – Discount%)/100

Selling price = Labeled price – Discount

Selling price = Cost price + Profit

Calculations:

Calculating discount amount first

⇒ Discount = (10 ÷ 100) × Rs. 3,500

⇒ Discount = Rs. 350

⇒ Selling price = Rs. 3,500 – Rs. 350

⇒ S.P. = Rs. 3,150

⇒ C.P. = Rs. 3,150 – Rs. 250

⇒ C.P. = Rs. 2,900

∴ Cost price of the yarn is Rs. 2,900

Given:

Selling price = cost price – 25% of cost price

Calculation:

Let the cost price for 1000 gram = Rs. 1000

Selling price of 1000 gram = Rs. 750

But, due to false weighing

Selling price of 600 gram = Rs. 750

Cost price of 600 gram = Rs. 600

So, there is a profit

Profit = Rs. 750 – Rs. 600

⇒ Rs. 150

Profit% = [(150/600) × 100]%

⇒ 25%

Given:

X to Y = 20% profit

Y to Z = 25% profit

Final C.P. = Rs 1500

Formula used:

S.P. = C.P. + Gain

S.P. = C.P. – Loss

Profit% = (Profit/C.P.) × 100

Calculation:

Let, an unit = X

⇒ P sells at 1/5 profit. Hence, C.P. = 5 × X and S.P. = 6 × X

⇒ Q sells at 1/4 profit. Hence, C.P. = 4 × X and S.P. = 5 × X

⇒ Cost price of X = (5 × 4 × X)

⇒ Cost price of Z = (6 × 5 × X)

⇒ C.P. of Z = 30 × X and C.P. of X = 20 × X

Now, final C.P. = 1500

⇒ 30 × X = 1,500

⇒ X = 50

⇒ C.P. of X = 20 × 50

⇒ C.P. of X = 1000

∴ Cost price of article at X is Rs 1000

Given:

Selling price at 20% loss = Rs. 3200

Calculations:

Selling price at 20% loss = Rs. 3200

⇒ At (100 - 20)% = 80% , selling price = Rs. 3200

⇒ At (100 + 25)% = 125%, selling price = Rs. 3200 × (125/80)

⇒ At (100 + 25)% = 125%, selling price = Rs. 5000

∴ The selling price of article when sold at 25% gain is Rs. 5000.

GIVEN:

A sold an article to B at a profit of 20%, B sold that article to C at a profit of 10% and C sells that article to A again at a loss of 25%.

FORMULA USED:

SP = CP × (1 - Loss %/100)

SP = CP × (1 + Profit %/100)

CALCULATION:

Let the CP for A be 100

So,

SP for A and CP for B = 100 × 1.2 = 120

SP for B and CP for C = 120 × 1.1 = 132

SP for C and CP for A = 132 × 0.75 = 99

Now if we take a look at the three transactions we will find out CP for A is 99 and SP for A is 120 so profit is 21.

But this profit percentage will be calculated at the original CP for A that is Rs. 100

So

Profit% = 21/100 × 100 = 21%

Given∶

Loss = 6%

Formula used∶

Selling price = cost price – loss

Selling price = cost price + profit

Calculation∶

Let the cost price is Rs. x

Selling price = x – 6% of x

⇒ 94x/100

New selling price = x + 15% of x

⇒ (94x/100) + 15750 = x + 15% of x

⇒ (94x/100) – (115x/100) = -15750

⇒ 21x/100 = 15750

⇒ x = Rs. 75,000

∴ The cost price is Rs. 75,000.