**Topics :**

- Simplification
- Number Series
- Percentage
- Profit and Loss
- Simple Interest and Compound Interest
- Ratio and Proportion
- Time and Work
- Time Speed and Distance

## #1 Simplification

**Sol :**

(2

^{3})

^{12}÷ (2

^{4})

^{2}of (2

^{5})

^{3}× 16 = 2

2

^{36 }÷ 2

^{8}of 2

^{15}× 2

^{4}= 2

^{?}

2

^{17}= 2

^{?}

? = 17

**Q2. **

108 ÷ 36 of ^{1}/

_{4}+

^{2}/

_{5 }× 3

^{1}/

_{4}= ?

**Sol :**

108 ÷ 9 +

^{2}/_{5}×^{13}/_{4}= ?12+

^{13}/_{10}? = 13

33^{3}/_{10}**Q3.**

^{1}/

_{3}% of 633 + 129 = 66

^{2}/

_{3}% of = ?

**Sol :**

^{1}/

_{3}× 633 + 129 =

^{2}/

_{3}×?

( 211+129 )×

^{3}/

_{2}= ?

? = 340×

^{3}/

_{2}= 170×3 = 510

More Tricks on Simplification and Download PDF : Click Here

## #2 Number Series

Basic Concept Starts From Here : Click Here

### Q1.

In each series only one number is wrong. Find out the Wrong number.- 5531, 5506, 5425, 5304, 5135, 4910, 4621
**(IBPS PO 2012)**

**Hint: -7**

^{2}, -9^{2}, -11^{2}

- 1, 3, 10, 36, 152, 760, 4632
**(IBPS PO 2012)**

**Hint :**×1+2, ×2+4, ×3+6 ...

- 4, 3, 9, 34, 96, 219, 435
**(IBPS PO 2012)**

**Hint : +1**+3

^{3}-2 , +2^{3}-2 ,^{3}-2, ...

- 5, 7, 16, 57, 244, 1245, 7506
**(Allahabad Bank PO 2010)**

**Hint :**×1+1

^{2},×2+2

^{2}

- 2.5,3.5,6.5,15.5,41.25,126.75
**(Allahabad Bank PO 2010)**

**Hint :**×

^{1}/2+

^{1}/2, ×1+1 , ×

^{3}/2+

^{3}/2 ....

## #3 Percentage

Basic Concepts Starts Here : Click Here

By using formula

less% = r/100+r ×100 = 10/100+10 × 100

= 10/110 ×100 = 9 1/11%

Let the original fraction be x/y then -

Given Fraction = 5/8

Original fraction = 5/8×80/110

= 5/11 Ans.

### Q1.

If the income of Ram is 10% more than that of Shayam's income. How much % Shyam's income is less than that of Ram's income ?**Method I.**By using formula

less% = r/100+r ×100 = 10/100+10 × 100

= 10/110 ×100 = 9 1/11%

**Method II.**### Q2.

A man spends 40% on food, 20% on house rent, 12% on travel and 10% on education. After all these expenditure he saved Rs. 7200. Find the amount spent on travel ?

**Method I.**

Let total income x

total expenditure

= x × (40%+20%+12%+10%)

= x × 82%

Total saving = x - x × 82%

= x × 18%

Then x × 18% = 7200

x = 7200/18×100 = 40,000

Expenditure on travel = 12%

x × 12% = 40,000×12/100 = Rs. 4800

**Method II.**

Total income = 100% - represent total

100% -82% = 18% (saving)

Expenditure on Travel = 7200/18×12

= 4800

### Q3.

When numerator of a fraction is increased by 10% and denominator decreased by 20% the resultant fraction becomes 5/8. Find the original fraction ?**Method I.**Let the original fraction be x/y then -

**Method II.**Given Fraction = 5/8

Original fraction = 5/8×80/110

= 5/11 Ans.

### Q4.

If the length of a rectangle is increased by 20% and breath is decreased by 10%. Find the net% change in the area of that rectangle.**Sol:**

net% change = x+y+ x×y/100

(+20)×(-10)/100

= +10-2

=8

Increase % = 8% Ans.

### Q5.

A reduction of 10% in the price of tea would enable and purchase to obtain 3 Kg. more for 2700 Rs. Find the reduced rate (new rate ) of tea ?Sol :

10% 2700 = Rs. 270

Rs. 270 is the rate of 3 kg. of tea

1 kg of tea = Rs. 90/- kg,

## #4 Profit and Loss

Basic Concept Starts Here : Click Here

**Statement**

A purchase an article at Rs 40 Rs. and sells it to B at rs. 50 and B sells its to C at Rs. 30**For A,**Profit = 50-40 = 10

**For B,**Loss = 50 -30 = 20

**For A,**P =SP-CP

**For B,**L= CP-SP

**For A,**Percent Profit = Profit of A/CP of A×100

**For B,**Percent loss = Loss of B/CP of B×100

**For A,**10/40×100 = 25%

**For B,**20/50×100 = 40%

P% = P/CP×100

L% = L/CP×100

**Q1.**

A person purchased an article for Rs. 80 and sold it for Rs. 100.Find his % profit.

Sol:

CP of the article = Rs. 80

SP of the article = Rs. 100

Profit of the person = 100-80 = Rs. 20

% Profit of the person = Profit /CP×100

%P = 20/80×100

%P = 25%

**Trick:**

%P = 20/80×100 = 25%

### Q2.

A dishonest shopkeeper sells goods at his cost price but uses a weight of 900 gm for a kg. weight. Find his gain percent.

Sol:

The Cp of Shopkeeper = 900 gm

The Sp of Shopkeeper

= 1000 gm ( 1kg = 1000 gm )

The profit of shopkeeper

= 1000 -900 = 100 gm

% profit shopkeeper

=

^{Profit of shopkeeper}/_{CP of shopkeeper}×100%P =

^{100}/_{900}×100 = 11^{1}/_{9}%### Q3.

A person got 5% loss by selling an article for Rs. 1045. At what price should the article be sold to earn 5% profit ?

Sol:

Trick :

New SP = 1045/95×105 = 1155

### Q4.

A person sold an article at profit of 12%. If he had sold it Rs. 3.60 more, he would have gain 18%. What is the cost price ?

Sol:

Trick :

CP = 3.60/6×100 = Rs. 60

### Q5.

If the CP of 12 articles is equal to the SP of 9 articles. Find the gain or loss.

Sol : Let the CP of each article be Rs. 1

Then CP of 9 articles = Rs. 9

SP of 9 articles = Rs. 12

Gain % =

^{3}/9×100 = 33^{1}/_{3}%## # 5 Simple and Compound Interest

Basic Concept Starts From Here : Click Here

### Q1.

At what rate of interest per annum will a sum double itself in 8 years ?Sol:

Trick :

### Q2.

A sum of money double itself at compound interest in 15 years. In how many years will it become eight times.Trick :

t

_{2}= 45 years## #6 Ratio and Proportion

### Q1.

The ratio between the length and the breadth of a rectabgular field is 5:4 respectively. If the perimeter of that field is 360 meters. what is the breadth of that field in meters ?Sol :

Perimeter = 2(5+4) = 18

Mean value of 18 = 360

Breadth =

^{360}/

_{18}× 4 = 80 meters

### Q2.

A bag contains 50 P, 25 P and 10 P coins in the ratio 5:9:4 amounting to Rs. 206. Find the number of coins of each type.Sol:

Let the number of 50P,25P and 10P coins be 5x,9x and 4x respectively

5x/2+9x/4+4x/10 = 206

50x + 45x + 8x = 4120

103x = 4120

x = 40

No. of 50 P coins = 5×40 = 200

No. of 25 P coins = 4×40 = 160

No. of 10 P coins = 9×40 = 360

Sol:

Let the quantity of alcohal and water be 4x liters and 3x liters respectively.

4x/

8x =20

x = 2.5

Sol:

No. of 10 P coins = 9×40 = 360

### Q3.

A mixture contains alcohol and water in the ratio of 4:3. If 5 liters of water is added to the mixture the ratio becomes 4:5. Find the quantities of alcohol in the given mixture.Sol:

Let the quantity of alcohal and water be 4x liters and 3x liters respectively.

4x/

_{3x+5}= 4/58x =20

x = 2.5

### Q4.

A:B = 5:9 and B:C = 4:7 Find A:B:C.Sol:

## #7 Time and Work

### Q1.

A can finish a work in 24 days , B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days.The remaining work was done by A in ?

**(S.S.C.2003)**Sol:

X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last ?

**(Bank PO,2004)**

Sol:

### Q3.

A work twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is ?

Sol :

## #8 Time, Speed and Distance

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