solve all types of percentage problem with short trick or method without using formula and collect all the SSC, railway and all government oriented questions.

Percentage questions play a very important role not only in exam but in our daily life also. Though the percentage is used is many maths aptitude topic, we study it as a separate unit due to its importance by the exam point of view. Strong command over percentage indicates the strong command over half of maths aptitude. Percentage questions are quite confusing for many people. Whenever we try to solve percentage questions by using pen and paper they become even more time taking.

Hence to overcome this problem we are sharing some of the best maths trick to solve percentage questions just in 2-3 seconds.

Let us understand type 1 of Percentage Questions with an example:

Question: If salary of A is 50% greater than the salary of B. So how many lesser the salary of B than the salary of A ?

Solution using our short trick:

Let always suppose the salary of B = 100.

Note:

• If salary of A > B then Add (+) the greater percent of salary of A in salary of B.
• If salary of A < B then subtract (-) the lesser percent of salary of A from salary of B.

As given in the question salary of A is 50% greater than salary of B,

So,

Salary of A = 100 + 50 = 150

Now we know that salary of B is ’50’ less than the salary of A which is ‘150’.

So,

This is the required answer.

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Shortest Trick for this type of Percentage Questions:

Below we are sharing some some standard combination of results (सीधे याद रखने योग्य परिणाम). A total of 90% of questions in exams asked from this topic (type 1) are from those results directly. If you remember those results you will not even take a second to tick the answer:

• 100% and 50% or (100)% and (100/2)%

• 50% and 33.3% or (100/2)% and (100/3)%

• 33.3% and 25% or (100/3)% and (100/4)%

• 25% and 20% or (100/4)% and (100/5)%

• 20% and 16.66% or (100/5)% and (100/6)%

उदाहरण:

1. यदि A की सैलरी B की सैलरी से 100% ज्यादा है तब B की सैलरी A की सैलरी से (100/2)% या 50% कम होगी.
2. यदि A की सैलरी B की सैलरी से (100/2)% या 50% ज्यादा है तब B की सैलरी A की सैलरी से (100/3)% या 33.33% कम होगी.
3. यदि A की सैलरी B की सैलरी से (100/3)% या 33.33% ज्यादा है तब B की सैलरी A की सैलरी से (100/4)% या 25% कम होगी.
4. यदि A की सैलरी B की सैलरी से (100/4)% या 25% ज्यादा है तब B की सैलरी A की सैलरी से (100/5)% या 20% कम होगी.
5. यदि A की सैलरी B की सैलरी से (100/5)% या 20% ज्यादा है तब B की सैलरी A की सैलरी से (100/6)% या 16.66% कम होगी.

इसी प्रकार:

1. यदि A की सैलरी B की सैलरी से (100/2)% या 50% कम है तब B की सैलरी A की सैलरी से (100)% या 100% ज्यादा होगी.
2. यदि A की सैलरी B की सैलरी से (100/3)% या 33.33% कम है तब B की सैलरी A की सैलरी से (100/2)% या 50% ज्यादा होगी.
3. यदि A की सैलरी B की सैलरी से (100/4)% या 25% कम है तब B की सैलरी A की सैलरी से (100/3)% या 33.33% ज्यादा होगी.
4. यदि A की सैलरी B की सैलरी से (100/5)% या 20% कम है तब B की सैलरी A की सैलरी से (100/4)% या 25% ज्यादा होगी.
5. यदि A की सैलरी B की सैलरी से (100/6)% या 16.66% कम है तब B की सैलरी A की सैलरी से (100/5)% या 20% ज्यादा होगी.

1-Questions based on increase

A-Ram^s income is 20% more than shyam^s  income.What % shyam^s income is less than Ram^s income?

Solution- Shyam^s income % less than Ram^s income =  100*20/120= 50/3%.

B- By a reason a man increases his expenditure by 40%.After end of that reason by how much % will be diminish his expenditure so that his expenses remain the same?

Solution- %decrease in expenditure = 100*40/140= 28.57%.

2- Questions based on decrease

A- The piece of sugar falls by 20% by how much percent should a consumer increase its consumption so that his expenditure remains unchanged?

Solution- % increase = 100*20/80 = 25%.

B- on multiplication of two numbers one number has decreased by 30% . How much % should the second number be increase so that the product be correct?

Solution- % increase of second number = 100*30 = 259/7%.

3- Questions based on decrease and increase both

A- Mohan decreased 15% his expenses and later on decreased by 5% more.How many % did his expense decrease?

Solution- percent change= -15-15+{-15*-15}/100= -19.25 % decrease.

B-The price of an article is reduced by 25% and it^s daily saly increased by 30%.Find the net % effect on daily sale?

Solution- percent change = -25+30+{-25*30}/100= 2.5 % decrease.

4- Question based on area

A- The radius of a circle is reduced by 5%. Find the % reduce in the area of circle?

Solution- % change in  area -5-5+0.25 = -9.75%.

B- If the diameter of a sphere is increased by 20% . By what% is its surface area increased?

Solution- % change in surface area = 20+20+400/100= 44%.

5- Question based on volume

A-Radius of a cylinder is 5% icreased and height is increased 10% .Find the % increase in volume of the cyinder?

Solution- % increase in two dimensions = 5+5+25/100=10.25% increase

                 % increase in three dimensions= 10.25+10+1.025 = 21.275% increase.

B- Diameter of a sphere is reduced by 10 % . By what % did its volume reduce?

Solution= % reduce in two dimensions= -10-10+1= -19% decrease

                  % increase in three dimensions = -19-10+1.9= -27.1% decrease.

6- Questions based on income and expense

A- gopal spends 30% of his income on grossery and 40% of remaining on travels. After this he spends 25% on education . If his annual income is rs. 2lakh.Find his annual savings?

Solution- Gopal^s saving = 200000*70/100*60/100*75/100 = 20*7*6*75 =63000.

B- A man spends 30 % of his income on education , 50% of remaining on ration. He gives rs-1000 for house  rent from remains. At last he saves rs- 1800. Find the mans monthly income?

Solution- Let mans monthly income is rs- X

                  X*70/100*50/100-1000= 1800

                  7x/20= 1000+1800=2800

                  So x= 2800*20/7= rs. 8000.

7-Question based on Population

A-The population of a town is 100000 it increases 10% per annum what will be
its population of the 3 years?

Solution- 100000[110/100]3= 100000[11/10]3

                100000*1331/1000=133100.

B-The population of mohans village is 6760 if it increases by 4 per present yearly then how much was the
population before 2 years?

Solution-6760 = P*676/625

               P= 6760*625/676= 6250.

8- Question based on fail and pass in exam

A-In an examination 60% student passed in mathematics 70% in English and 50 % I both subjects . what find the percentage of total who passed in both subjects?

Solution-% passed of students = 100-40-30+50= 150-70= 80 .

B-There were two papers in an examination of Hind,i 75% students in first paper, 55 and 35 per students in both the paper were failed.  how many%  student failed?

Solution- % passed students = 100-25-45-=35=135-70=65%

                So % of failed students = 100 – 65 = 35 %.

9- Miscellaneous questions

A- In a hostel 800 boys live. 75% of the boys play hockey and 50% play football.Each boy plays either hockey or football or both . how many boys play the both game?

Solution-let x boys play the both games

               So 800= 75 % of 800 + 50 % of 800 – x

               So 800 = 600 + 400 – x

               X = 1000-800 = 200

 B-In an office 70% employees like tea and 40% like coffee. Each  employee likesanyone or both . if 25 employees like both then how many employees are in theoffice?

Solution – Let there are X employees In the office

                 X= 70 % of X + 40 % of X-25

                 X = 70/100 * X + 40/100 * X – 25

                  X=7x/10+4x/10 – 25

                  X = 11x/10 – 25

                  11x/10 –x = 25 = 11x – 10x/10 = 25

                   So x/10 = 25 or x = 250.

Questions asked in ssc cgl examinations:

1-The length of a rectangle increase by 12% and the breadth by 10 % then the % increase in area? [ssccgl 2012]

2- A number is increased by 20 % and the decreasd by 20 % . Finally the number is ?[ssc 2014]

3- Ratan expenditures and savings are in the ratio  5 : 1. If his salary is increased by 25 % and saving by 15 % the percentage of increase in his expenditure is ? [ssc cpo 2012]

4- If a gets 25 % more than b and b gets 20 % more than c , then the share of c out of a sum of 740 is ? [ssc tax assistant 2009]

5- Out of total population of 5000 people in a village men increased by 10%  and women by 15 % .Now the total population becomes 5600 in a year . the women population in the village is originally ? [cpo si 2012].

6- The population of a town has been increasing at the rate of 10% every year . The present population is 121000. What was the population two years ago? [ssc tax assistant 2009]

7- Three fifth of two third of three seventh of a number is 150 . what is 60 % of tha number ?

8- A student scored 32 % marks in science subjects out of 300. How much should he score in 

language papers out of 200 if he is to get overall 46 % marks? [ssc cgl 2013].

multiplication tricks

                  multiplication trick

Any number × 99
example -
 99×35
 1st step -( 35-1)=34
2nd step- subtract 34 from 99
                 (99-34)=65
3rd step- combine both no.
    3465 is the answer.
     
 Any number × 11
example -
11×23
step 1- side 2 and 3 like 2 _3
step 2- then add 2 no. 5
step 3- then put 5 in between 2 and 3
answer is 253.

note carry case
11×76
step 1- side 7 and 6 like 7_ _6
step 2- then add 7 no. 6
step 3- if carry occure then (13) then take 3 and 1 as carry. then carry 1 is added to 7.
836
answer is 836.

HOW TO SOLVE PROFIT AND LOSS PROBLEMS VERY SHORTCUT WISE. WITHOUT USING ANY FORMULA. ITS A VERY VERY EASY TRICK

Hello friends myself Raj and today I am going to tell you how to solve all the major problems about profit and loss. But before I am starting my short tricks you have to know about basics of profit and loss and all the basic formulas.  After you learn all the basic tricks of it then you can easily solve all of yours problems in profit and loss.

Here is a video of short tricks of profit and loss. If you want to see than see. otherwise you can continue with this article.

• What is C. P? 
•      C.P stands for cost price.  The price           what the buyer gives to seller.

• What is S.P?                                                   S.P stands for selling price. The cost what the seller sells any article to the buyer. 

• What is profit?                                          Profit is when C.P is less than S.P(C.P<S.P). 

• What is loss?                                          Loss is when C.P is greater than S.P. (C.P>S.P). 

• R% profit = (100+R)%                            This means if 20% profit is then we imagine if C.P 100.then S.P = 120

• R% loss = (100-R)%                                This means if 25% loss is then we imagine that if C.P 100. Then S.P is 75.

• IN PRICE :                                                    A gain % or loss% counted on cost price or 100

• Gain=S.P-C.P
• Loss=C.P-S.P
• If C.P and loss is given then                   S.P= C.P *(100-R) /100
• If C.P and profit is given then                      S.P= C.P*(100+R)/100
•   If S.P and loss is given then                        C.P=S.P*100/(100-R)
• If S.P and profit is given then                     C.P=S.P*100/(100+R)

                      SOME EXAMPLES

1.   S.P=Rs. 120/-

       Loss=Rs. 30/-

       Loss% is what? 

Solution - Here S.P and loss is given then we easily can get C.P here.  So           C. P=120+30=150

NOTE :- Profit and loss always count on C.P  note this in your mind. 

 So when C.P is 150 then S.P=120

 Then when C.P =150, Loss=30

            When C.P=1     , Loss=30/150

           When C.P=100, Loss=(30/150)/100

                        Loss%=20%  (Answer)

2.   C.P=Rs. 680/-

      Gain=25%

      S.P=? 

 SOLUTION - C.P=680 

                        S.P= 680*(100+25)/100

                        S.P=850 Rs (Answer)

3.   C.P=Rs. 450/-

      S.P=Rs. 600/-

     Gain %=? 

Solution - C.P=450

                   Gain=S.P-C.P=600-450=150/-

                    c. p=   450=150 Gain

                    C.P=     1   =150/450

                     C.P=   100=(150/450)/100

                      =33.3%     (answer)

IN ARTICLE
Gain or loss percent(%)  always count on S.P or 100.

EXAMPLES
4. A man buys 12 lemons for a rupee and sell 15 lemons for a rupee.  Find the loss or gain %.
Solution - 

                  C.P       S. P
                    12        15
           S.P=15, Loss =3
           S.P =1, Loss =3/15
           S.P = (3/15)*100
                  =20%   (ANSWER)


5.    The cost of 25 tables is equal to the S.P of 20 tables.  Find the gain %
Solution -  This means
C.P*25 TABLES=S.P * 20 TABLES
C.P/S.P=20/25
              =4/5
here 4 is C.P and 5 is S.P.  As we know profit and loss is always counts on c.p so that here profit is 1.
so (1/4)*100

     =25% profit (ANSWER) 

6.   a man sold two radios at Rs.4800 each. On one he gains 20% and on the other he loses 20%. Find the gain or loss percent in the whole transaction?Solution :- 

So friends in this type of questions always there is loss.

This question has a very short trick 

that simply square the rate and devide it to 100.

  (20)²/100=4% loss

7.   On selling an article for Rs.550, a man gains 10%. What should be the selling price, if desired profit is 20%?

Solution:

SP= 550×(100 + 20 / 100 +15)

= 550 × 120/110 = Rs.600( ANSWER)

8.   Ram sold a cow for Rs.136 and thus lost 15%. At what price he should have sold it to gain 15%?

Solution:

New selling price = 136 × (100+15)/(100-15)

= 136 × 115/85 = Rs.184

9.   Shopkeeper buys 25 tables and 10 chairs for Rs. 7000 sells, table at 10%, chair at 12% profit. If he gets 7740 find CP of table and chair?

Solution:

(If Both Increase by 10% then overall increment will be10% i.e. 10% of 7000/- which is Rs.700. But profit = 740. This extra 40/- is due to 2% of chair)

2% Chair –> 40/-

100% C(10) –> 2000

1 chair = 2000/10 = 200

So all table (25) = 5000/-

1 table = 5000/25 = 200/-

10.   A man purchased two articles for total cost of Rs.9000. He sold the first article at 15% profit and the second at 12% loss. In the bargain, he neither gained nor lost anything. Find cost price of the first article.
Solution :-

Ratio of cost price of the first and the second article = 12 : 15 = 4: 5

Cost price of the first article = 4/9 ×9000 = Rs.4000. 

 To find the percent gain or loss, divide the amount gained or lost by the cost price and multiply it by 100. 
11.   Example: A toy that cost 80 rupees is sold at a profit of 20 rupees. Find the percent or rate of profit.
Answer:
Gain/cost × 100 = % profit.

20/80 × 100 = 25%. - Answer       


           To find the loss and the selling price when the cost and the percent loss are given, multiply the cost by the percent and subtract the product from the cost.

12.   Example: A damaged chair that cost Rs.110 was sold at a loss of 10%. Find the loss and the selling price.

Answer:

Cost x percent loss = loss.

110 x 1/10 = 11, loss.

Cost - loss = selling price.

110 - 11 = 99, selling price.

Profit and Loss Based on Selling Price

To find the profit and the cost when the selling price and the percent profit are given, multiply the selling price by the percent profit and subtract the result from the selling price.

13.   Example: A toy is sold for Rs. 6.00 at a profit of 25% of the selling price. Separate this selling price into cost and profit.

Answer :

Selling price x % profit = profit.

Selling price = profit + cost.

6.00 x .25 = 1.50, profit.

6.00 - 1.50 = 4.50, cost.             


               To find the loss and the cost when the selling price and the percent loss are given, multiply the selling price by the percent loss and subtract the result from the selling price.

14.   Example: At a sale, neckties selling at Rs. 50.00 are sold at a loss of 60% of selling price. What is the loss and the original cost?

Selling price x % loss = loss.

Selling price + loss = cost.

50.00 x .60 = 30.00, loss.

50.00 - 30.00 = 20.00, cost.

  To find the selling price when the cost and the percent loss are given, add the percent loss to 100% and divide the cost by this sum.

15.   Example: Socks that cost 7.00 per pair were sold at a loss of 25% of selling price. What was the selling price?

Answer: Cost / (100% + % loss) = selling price.

7.00 / 1.25 = 5.60, selling price.

To find the selling price when the profit and the percent profit are given, or to find the selling price when the loss and the percent loss are given, divide the profit or loss by the percent profit or loss.

Note: This rule should be compared with the one under Profit and Loss Based on Cost. The two rules are exactly similar except that in one case 100% represents cost while in the other case 100% represents selling price.

16.   Example: A kind of tape is selling at a profit of 12% of selling price, equal to 18 per yard. What is the selling price of the tape?

Answer: Profit / % profit = selling price.

18 /.12 = 1.50 selling price.

To find the percent profit or loss, divide the amount gained or lost by the selling price.

17.   Example: A candy bar sells for 1.30 at a profit of 65. What percent of profit on selling price does this represent?

Answer: Gain / selling price = % profit.

65 / 1.30 = .5 or 50% profit.

Mark-up Price

Generally the SP is less than the marked price (MP) the difference MP – SP is known as discount, D.

Discount = M P – S P

Discount %, D% = (Discount) / (M P) ×100

To reduce percent loss on cost to percent loss on selling price, divide percent loss on cost by 100% minus percent loss on cost.

18.    Example: 20% loss on cost is what percent loss on selling price?

Answer:

% loss on cost / (100% - % loss on cost) = % loss on selling price.

0.20 / 80 = .0025 or 25% loss on selling price

To reduce percent loss on selling price to percent loss on cost, divide percent loss on selling price by 100% plus percent loss on selling price.

19.   Example: 20% loss on selling price is what percent loss on cost?

Answer:

% loss on selling price / (100% + % loss on selling price) = % loss on cost.

.20 / 1.20 = .16666 or .16.67% loss on cost.

To reduce percent mark-up (percent profit on cost) to percent profit on selling price, divide percent mark-up by 100% plus percent mark-up.

20.   Example: A coat marked up 60% carries what percent of profit on selling price?

Answer : % profit on cost / ( 100% + % profit on cost ) = % profit on selling price.

.60 / 1.60 = .375 or 37.5% on selling price.

Here we are providing you all the types of questions that have been asked in SSC Exams and How to solve it in an Easy way with  Grade Stack methods:-

Type 1: 

The cost price of 40 articles is the same as the selling price of 25 articles. Find the gain per cent. (CGL-2012)

(a) 65%                                

(b) 60%

(c) 15%                                

(d) 75%

Answer: (b) Gain per cent

=(40-25)/25×100

=15/25×100=60%

Grade Stack methods

In Above question We take x = 40 , y = 25

Then Gain % = (x –y) x 100/ y

Type2: 

Bananas are bought at the rate of 6 for Rs. 5 and sold at the rate of 5 for Rs. 6. Profit per cent is:  (CGL-2004)

(a) 36%                                

(b) 42%

(c) 44%                                

(d) 48%

Answer : (c) To avoid fraction, let the number of bananas bought

LCM of 5 and 6 = 30

CP of 30 bananas

= 5 x 5 = Rs. 25

SP of 30 Bananas = 6 x 6

= Rs. 36

Profit = Rs. (36-25) = Rs. 11

Profit %

= 11/25×100=44%

Grade Stack Method

[(6 x 6 -5x 5)/ (5 x 5)] x 100 = 44%

Type 3:

A man bought oranges at the rate of 8 for Rs 34 and sold them at the rate of 12 for Rs. 27. How many oranges should be sold to earn a net profit of Rs 45? (CGL-2011)

(a) 90                                    

(b) 100

(c) 135                                  

(d) 150

Answers: (a) Let the man buy 24 (LCM of 8 and 12) oranges.

C.P. of 24 oranges  = 34/8  ×24 = Rs. 102

S.P. of 24 oranges = 27/12×24=  Rs. 114

Gain = 114 – 102 = Rs. 12

Rs. 12 = 24 oranges

Rs. 45 =  24/12×45= 90 oranges

Type 4: 

A shopkeeper earns a profit of 12% on selling a book at 10% discount on printed price. The ratio of the cost price to printed price of the book is ? (CGL-2013)

(a) 45 : 56                                

 (b) 50 : 61

(c) 90 : 97                                 

(d) 99 : 125

Answer:  (a) C.P. of the book = Rs. x

Printed price = Rs. y

(y×90)/100=x × 112/100

x/y=90/112=45/56

Type 5: 

A dealer sold two types of goods for Rs 10,000 each. On one of them, he lost 20% and on the other he gained 20%. His gain or loss per cent in the entire transaction was (CGL-2012)

(a) 2% loss                          

(b) 2% gain

(c) 4% gain                         

(d) 4% loss

Answers:  (d) Here, S.P. is same, Hence there is always a loss. Loss per cent =(20×20)/100=4%

 Gradestack Trick

Loss % = (n^2)/100= (20)^2/100= 4%

Where n= 20

Type 6: 

On selling an article for Rs170, a shopkeeper loses 15%. In order to gain 20%, he must sell that article at rupees: (CGL-2013)

(a) 215.50                           

(b) 212.50

(c) 240                                

(d) 210

Answer ; (c) C.P. of article = (200×120)/100 = Rs. 240

Type 7:

An article is sold at a loss of 10%. Had it been sold for Rs. 9 more, there would have been a gain of 12 1/2% on it. The cost price of the article is (CGL – 2002)

(a) Rs. 40                                             

(b) Rs. 45

(c) Rs. 50                                             

(d) Rs. 35

Answers: (a) Let the cost price of the article = Rs. x

S.P. at 10% loss

= x×90/100= Rs. 9x/10

1. P. at 12 1/2 % gain

x  × (100+12 1/2)/100 = Rs. 225x/200

According to the question

9x/10 + 9 = 225x/200

180x + 1800 = 225x

x = Rs. 40

Type 8: 

A sells a suitcase to B at 10% profit. B sells it to C at 30% profit. If C pays Rs 2860 for it, then the price at which a bought it is (CGL-2013)

(a) 1000                                               

(b) 1600

(c) 2000                                               

(d)  2500

Answer:  (c) If the C.P. of the suitcase for A be Rs. x, then

x ×110/100×130/100=2860

x=(2860×100×100)/(110×130) = Rs. 2000

Type 9: 

Arun marks up the computer he is selling by 20% profit and sells them at a discount of 15%. Arun’s net gain percent is 

(CGL-2013)

(a) 4                                      

(b) 2

(c) 3.5                                   

(d) 2.5

Answer (b)

Gradestack method:

r1 = 20 , r2 = 15

Formula = r1 – r2 – (r1 x r2)/100

(20-15-(20×15)/100)

= 20 -18 = 2%

Type10:

A tradesman sold an article at a loss of 20%. If the selling price had been increased by Rs. 100, there would have been a gain of 5%. The cost price of the article was: (CGL-2004)

(a) Rs. 200                                          

(b) Rs. 25

(c) Rs. 400                                          

(d) Rs. 250

Answer  (c) Let the C.P. of article be Rs. x.

105% of x - 80% of x = Rx. 100

25% of x = Rx. 100

x = Rs. (100×100)/25

= Rs. 400