Chapter 1: PercentageDEFINITION : a percentage is a number or ratio expressed as a fraction of 100.

if we have to convert percentage into fraction than it is divide by 100.Example 1 :- if we write 45% then its equal to 45/100 or in fraction 9/20 or in decimal 0.45

if we have to convert fraction into percentage we have to multiple with 100.Example 2 :- if we write 3/5 in fraction it is equal to 60%                                    3/5x100=60.READ AND LEARN FOLLOWING TABLE as also known as conversion table of percentage. Learn this table it help you a lot to solve many problem.

the following fraction in red colour are MOST IMPORTANT.

Fraction Percentage1/1 100%1/2 50%1/3 33.33%1/4 25%1/5 20%1/6 16.66%1/7 14.28%1/8 12.5%1/9 11.11%1/10 10%1/15 6.66%1/20 5%1/25 4%1/30 3.33%1/40 2.5%1/50 2%1/60 1.66%1/75 1.33%1/80 1.25%1/90 1.11%1/100 1%

by this conversion table we can change fraction into percentage and percentage into fractionEX:- if we have to find 2/5 in %?In the table we know that 1/5=20%then, if we multiply both by 2then we have 1/5x2 = 2x20%answer is 2/5 = 40%so, you only to know basic fraction and percentage that given above.

in the inverse Ex. If we have to find out 1/15 fraction in percentage%?

In the table we have 1/5 = 20%then both side multiple by 1/3we get 1/15 = 6.66%

SOME BASIC QUESTION THAT IS ALWAYS ASKED IN THE EXAMSTYPE 1. if there is increase of X% and subsequently X% decrease then there is always loss / decrease in the condition.

ex. If rohan salary is increase by 50% and subsequently decrease by 50%. How much percentage loss? By trick ----  50x50/100= 25% decrease/loss

TYPE 2.if A is P% more than B. then B is less than by A  with P/(100+P)x100

ex. If radha earning is 25% more than sita. Then sita earning is how many percentage less then by radha?ans. By trick ---- 25/(100+25)x100=20%   TYPE 3.If A is P% less than B. then B is more than by A  formula: P/(100-P)x100

ex. If golu age is 20% less than gita than gita age is how many percentage more than golu? By trick ---- 20/(100-20)x100=25%

TYPE 4.if there is p% increase in price . how much % decrease his consumption so that his expenditure on it does not change. Formula: P/(100+P)x100

ex. If petrol price increase by 25%. How much percentage a person reduced his consumption so that his expenditure on it does not increase? ans. 25/(100+25)x100=20%

TYPE 5. if there is p% decrease in price . how much % increase his consumption so that his expenditure on it does not change. Formula: P/(100-P)x100

ex. If there is 30% decrease in eggs price. How much a person increased his consumption so that his expenditure on it does not increase? ans. 30/(100-30)x100=42.85

TYPE 6.Ex. If suman need 36% minimum mark to passed a exam but she score 24% mark and fail by 9 marks. What is the total mark?ans. Difference in % = difference in mark In that 36%-24%=12%that is 12%=9marksso, total mark = 9/12x100= 75

Profit And Loss

Type 1:- The ratio of the cost price and the selling price is 4:5. The profit percent is?a. 10 b. 20 c. 25 d. 30Ans:- 25

 profit is always calculated on cost priceso,  c.p=4 , s.p=5

      Profit=s.p-c.p,  5-4=1  profit %=  profit/cost price * 100, then, 1/4*100= 25

Type 2:- If on selling 12 notebooks a seller makes a profit equal to selling price of 4 notebook, what is his profits percentage?

a.        16.2/3b. 25 c. 50 d. None of theseAns:-50

 if there is profit on selling item = selling price of an article        To find profit %, simply minus 12 from 4= 8        Profit % = 4/8*100=50

Type 3:- A vender loses the selling price of 4 oranges on selling 36 oranges his loss percentage is?a. 10 b. 11.1/9 c. 12.1/2 d.  None of theseAns:-10

  if there is loss on selling item = selling price of an article            to find loss%, simply add 36 to 4 = 40

  Loss % = 4/40*100 = 10

Type 4:- Some article were brought of 6 for rs. 5. And sold  at 5 for rs. 6. Gain percentage is/a. 30 b. 33.1/3 c. 35 d. 44Ans:-44  

Type 5:- A vender by selling 12 toffee for a rupee. A man loses 20%. How many for a rupee should he sell to get a gain of 20%?

a. 10b.  20 c. 8 d. 12Ans:- 8

12 toffee for rs 1 loss 20% then           c.p = 1*100/80 = 5/4    on this price we have to gain profit of 20%          So, 5/4* 120/100 = 3/2

         If for Rs. 2/3 we have 12 toffee then for rs 1 we have         = 12x2/3=8

Type 6:- A sell a bicycle of to B at a profit of 20%. B sell it to C at profit of 25%. If C pays rs. 225 for it the cost price of bicycle is?

a. 110 b. 120 c. 125 d. 150Ans:- 150

 let cost price be X then,          x.120/100 . 125/100= 225 , by solving, then X equal to 150

Type 7:- A shopkeeper professes to sell his goods at cost price but uses a weight of 800gm instead of 1kg. thus he makes a profit of?

a. 20% b. 16.2/3 c. 25 d. 50Ans :- 25

Type 8 :- A shopkeeper cheats to the extents of 10% while buying as well as selling by using false weight his total gain is ?

a. 10% b. 11% c. 20% d. 21%Ans :-21%

Type 9 :- An article when sold at a gain of 5% yields rs. 15 more than when sold at a loss of 5%. Its cost price would be

a. 150 b. 200 c. 250 d.300Ans:-150difference between gain % and loss% equal to 10%

            then, 10% = rs. 15        100% = rs. 150 , that is your cost price

Type 10:- The price of an article has been reduced by 25%. In order to restore the original price the reduced price must be increased by?

a. 25% b. 30% c. 33% d. 33.1/3%Ans:-33.1/3%

Type 11:- An article was sold at 16% gain. Had it been sold for rs. 200 more, the gain would have been 20% then the cost price of the article is?

a. 5000 b. 4800 c. 4500 d.5200Ans :- 5000

difference in gain % equal to 200,        Then  20%-16%=4%

               4%= 200 then,        100%= 5000 that is your cost price of the article

Work and Time

Square Roots

FIRST CASE:-  NUMBER WITH LAST DIGIT 5

SECOND CASE:- SQUARE BETWEEN 30 TO 50

THIRD CASE:- SQUARE BETWEEN 50 TO 80

FOURTH CASE:- SQUARE BETWEEN 80 TO 100

FIFTH CASE:- SQUARE BETWEEN 100  TO 130

MOCK TESTQ1. Find the square of 95?a. 9125 b. 9025 c. 9225 d. 9175

Q2. Find the square of 42?a. 1763 b. 1764 c. 1765 d. 1766

Q3. Find the square of 79?a. 6233 b. 6255 c. 6241 d. 6251

Q4. Find the square of 121?a. 15252 b. 12625 c. 14625 d. 14641

Q5. find the square of 98?a. 9604 b. 9609 c. 9603 d. 9600

Cube Roots

SIMPLE INTEREST

We have using these BASIC formulas S.I. = PxRxT / 100

BUT there are some example how these shortcut tricks that

Type 1.In how many years will a sum of money double itself at 12% per annum?a. 6years 6 months b. 7 years 6 months c. 8 years 3 months d. 8 years 4 months

Type 2. at what rate of percent of simple interest will a sum of money double itself in 12 years?a. 8% b. 8.1/3% c. 8.1/2% d. 9.1/2%

Type 3.The rate at which a sum become four times of itself in 15 years at simple interest will be?a.15% b. 17.1/2% c. 20% d. 25%

Type 4.if a sum of money at simple interest double in 6 years. it will become 4 time in ?a. 12 years b. 14 years c. 16 years d. 18 years

Type 5.How long will it take a sum of money invested at 5% p.a. by simple interest to increase it value by 40%?a. 5 years b. 6 years. c. 7 years d. 8 years

COMPOUND INTEREST SHORTCUT TRICKS

Type 1.a sum of money place at compound interest double itself in 5 years. It will become 8 times itself at same rate of interest in ?a. 7 years b. 10 years c. 15 years d. 20 years

Type2.By C.I. at 10 % p.a. a sum increased to 2662 in 3 years what will be the principal amount ?a. 1000 b. 1500 c. 2000 d. 2500

Type 3.

In C.I, what will be the rate of interest if a sum becomes 1331 in 3 years?a. 100b.1000c.10000d. none of these