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%

(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%

(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

(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

(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

(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

(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

(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

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

(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

(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

(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

solve all the mathematical problems in short tricks without formulae

Sunday, April 15, 2018

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

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

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 :-

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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.

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