Profit, Loss and Discount Short Trick लाभ हानि छूट ( बट्टा ) शार्ट ट्रिक
In this post we are going to give some most important short tricks of Profit and loss questions in Hindi as well as English language. This is very important tricks for those who want to clear various government departmental competitive examinations. because for checking accuracy and speed of candidates the examination board check through various aptitude chapters.
Term

Explanation

Cost Price:

The price at which a anything
is purchase is called Cost price;

Selling Price:

The price at which a anything is sell is
called Selling price.

Profit:

If selling price of anything is more than
its cast price then there is profit.

Loss:

If cost price of anything is more than
its selling price then there is loss.

Profit Percent:

If profit at per 100 rs is known
as % profit.

Loss Percent:

If
loss at per 100 rs is known as % loss.

Extra expanse:

In
bringing thing on its right place bus rent , train rent , porter rent
, taxi rent , rent of shop , salary of staff salary etc. Expenditure
of seller is called extra expanse.

Discount:

The
concession given by the seller on printed price s called discount.

Term

Formula

Profit=

Selling
price  cost price

Loss=

Cost
price  selling price

Cost price=

Selling
price  Profit

Cost price=

Selling
price + loss

Profit %=

{(Profit
/ cost price) x 100}%

Loss %=

{(Loss
/ cost price) x 100}%

PROFIT , LOSS AND DISCOUNT TRICKS AND TYPES
Profit
, Loss and Discount Type


Formula

If X is cost
price of a product is equal to selling price of Y products, then
1.
Profit
% = [{(X  Y) / Y } x 100] %
2.
Loss
% = [{(Y  X) / Y } x 100] %

Example: If cast price of 21 apples is equal to selling price of 15 apples , then find profit% ?
Most Important Questions and solution;
asked in previous year competitive exam


Q 1

Ex. 1. A man bought a horse and a carriage for Rs. 3000.
He sold the horse at a
gain of 20% and the
carriage at a loss of 10%, thereby gaining 2% on the whole. Find
the cost of the
horse.
Q : एक
आदमी ने 3000/ एक घोडा और एक गाड़ी खरीदी ; उसने घोडा 20% लाभ
पर और गाड़ी 10% हानी पर बेच दी; जिससे उसे 2% का
लाभ हुआ; घोड़े का क्रय मूल्य ज्ञात करो।

Solution

Let the C.P. of the horse be
Rs. x. Then, C.P. of the carriage = Rs. (3000 — x).
20% of x — 10% of (3000 — x) = 2% of 3000
x/5  (3000x)/10
= 60
=2x—3000+x = 600
= 3x= 3600
x= 1200.
Hence, C.P. of the horse =
Rs. 1200.

Q 2

Find the single
discount equivalent to a series discount of 20%, 10% and 5%.
Q: एकल छूट ज्ञात करो जो
लगातार 20%, 10% और 5% छूट के बराबर है।

Solution

Let marked price be Rs. 100.
Then, Net S.P. = 95% of 90% of 80% of Rs. 100
= Rs(95/100 x90/100 x 80/100) x 100 = Rs. 68.40.
... Required discount = (100 — 68.40)% = 31.6%.

Q 3

After getting two
successive discounts, a shirt with a list price of Rs. 150
available at Rs. 105. If the second discount is 12.5%, find the
first discount.
Q :
दो क्रमागत छूट के बाद एक कमीज़ के 105/ मे मिला जिसकी किमत 150/ थी। यदि दूसरी छूट 12.5% है तो दूसरी छूट ज्ञात करो।

Solution

Let the first discount be x%.
Then, 87.5% of (100 — x)% of 150 = 105
87.5/100 x (100x)/100 x 150 = 105
100x = (105x100x100) / 150x87.5)
=80
x = (10080)
= 20 First discount = 20%

Q 4

An uneducated retailer
marks all his goods at 50% above the cost price and
thinking that he will still make 25% profit, offers a discount of
25% on the marked
price. What is his actual profit on the sales?
: एक अनपड विक्रेता ने सभी वस्तुओ पर 50% बड़ा दिये क्रय मूल्य से। उसने
सोचा की शायद उसने 25% ही बड़ाये जिससे उसने 25% छूट भी दे दी। उसका लाभ
प्रतिशत ज्ञात करो।

Solution

Let C.P. = Rs. 100. Then,
marked price = Rs. 150.
S.P. = 75% of Rs. 150 = Rs. 112.50.
...
Gain% = 12.50%.

Q 5

A retailer buys 40
pens at the marked price of 36 pens from a wholesaler
If he sells these pens giving a discount of 1%, what is the
profit percent?
एक आदमी ने एक होलसेलर से 36 पेन की कीमत से 40 पेन खरीदे। अब उसने 1% छूट पर पेन बेचना शुरू किया , तो उसका लाभ ज्ञात करो।

Solution

Let the marked price of each
pen be Re. 1.
Then, C.P. of 40 pens = Rs. 36. S.P. of 40 pens = 99% of Rs. 40
= Rs. 39.60.
Profit%= (3.60/36 x lOO) % = 10%.

Q6

At what percentage
above the C.P must an artide be marked so as to gain
33% after allowing a customer a discount of 5%?
वह कीमत ज्ञात करो जिस पर
उसे 33% का लाभ मिले जब वह उस वस्तु पर 10% के साथ छूट भी दे।

Solution

Let C.P. = Rs. 100. Then,
S.P. =‘Rs. 133.
Let marked price be Rs. x
Then, 95% ofx= 133
95x/100=133
x = 133x 100/95J = 140
Marked
price = 40% above C.P.

Profit , Loss and Discount Type
Profit , Loss and Discount Trick2
Formula

If X product buy Y rupees and Y products is sold
at X rupees, then
1.
Profit % =
[{(X^2  Y^2) / Y^2 } x 100] %
2.
Loss % = [{(Y^2
 X^2) / Y^2 } x 100] %

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Profit , Loss and Discount Type
Profit , Loss and Discount Trick3


Formula

If X product is buy at
Y Rs and a product is sold at b Rs, then
1.
Profit
% = [{(bX  aY) / aY } x 100] %
2.
Loss
% = [{(aY  bX) / bY } x 100] %

Example: A fruit seller buy oranges at 5 rs per 3 and sold it at the rate of 4 rs per 2 oranges, then find profit% ?
Profit , Loss and Discount Type
Profit , Loss and Discount Trick4
 
Formula

1.
If on
selling X product , profit is equal to selling price of Y product , then
Profit % = [{Y / (X  Y) } x 100] %
2.
If on
selling X product , loss is equal to selling price of Y product , then
Loss % = [{Y / (X + Y) } x 100] %

Example: A shopkeeper sell 150 buttons and got profit of price of 25 buttons, then find profit% ?
Profit , Loss and Discount Trick5
Formula

1.
If
a businessmen at the time of buying used a defective weigh
machine and cheated of X% and at the time of selling cheated of X%, then
total profit percent
[{(100+X)^2
/ 100}  100]%
2.
If
a businessmen at the time of buying used a defective weigh
machine and cheated of X% and at the time of selling cheated of Y%, then
total profit percent
[{(100+X)(100+Y) / 100}  100]%

Example: A businessmen at the time of buying used a defective weigh machine and cheated of 10% and at the time of selling cheated of 10%, then find total profit% ?
Profit , Loss and Discount Type
Profit , Loss and Discount Trick6
Formula

Error%
or Profit% =
[(Error
/ wrong measurement) x 100]%

Example: A shopkeeper sold his product at the cost price , but at the place of 1kg weight he used 960 gm, then find profit percent% ?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick7


Formula

1.
If cost price of two products
is same and he got X% profit on first product and loss of X% on second then
there is no profit or loss.
2.
If selling price of two
products is same and he got X% profit on first product and loss of X% on
second then there is always loss and that loss% = [X^2 / 100]%.
3.
If selling price of two
products is same and he got P% profit on first product and loss of L% on
second then at this condition profit or loss % =
[{100(PL)2PL}/{(100+P)+(100L)}]%

Example: A person buy two book both at 80 rs , on selling one book he got profit of 15% and loss on selling second book , find profit or loss percent?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick8


Formula

Selling price of two products is same 
1.
If one of them is sold at P1%
profit and second is sold at profit of P2% , then
Cp1 : Cp2 = (100+P2)
: (100+P1)
2.
If one of them is sold at P%
profit and second is sold at loss of L% , then
Cp :CL = (100L) : (100+P)
3.
If one of them is sold at L1%
loss and second is sold at loss of L2% , then
CL1 : CL2 = (100L2)
: (100L1)

Example: Selling price of two fans is same , priented cost price of both is 2300 rs. one of them is sold at 10% profit and second is sold at profit of 20%, then find there cost price ?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick9


Formula

(i) Cost price
= (selling price x 100) / (100 + profit%)
(ii) Cost price
= (selling price x 100) / (100  loss%)
(i) Selling price
= cost price x (100+profit%) / 100
(ii) Selling price
= cost price x (100loss%) / 100

Profit , Loss and Discount Type
Profit
, Loss and Discount Trick10


Formula

1.
A product is sold at
X% profit, at a rs , if it will sold at Y% profit , then its selling price=
[{a x (100+Y)} / (100+X)] rs
2.
A product is sold at
X% loss, at a rs , if it will sold at Y% profit , then its selling price
= [{a x (100+Y)} /
(100X)] rs
3.
A product is sold at X%
loss, at a rs , if it will sold at Y% loss , then its selling price
= [{a x (100Y)} / (100X)] rs

Example: A electric iron is sold at 15% profit, if it will sold at 600 rs then we get 20% profit, then find its selling price?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick11


Formula

1.
A purchase a thing in
X rs and sell it to B at r1% profit and B sell it to C at r2% profit , if
cost price for C is Y rs , then
= X x [1 + (r1/100)] x [1 + (r2/100)] = Y
2.
A purchase a thing in
X rs and sell it to B at r1% profit and B sell it to C at r2% loss , if cost
price for C is Y rs , then
= X x [1 +
(r1/100)] x [1  (r2/100)] = Y
3.
A purchase a thing in
X rs and sell it to B at r1% loss and B sell it to C at r2% loss , if cost
price for C is Y rs , then
= X x [1  (r1/100)] x [1  (r2/100)] = Y

Example: A purchase a cycle and sell it B at 20% profit and B sell it to C at 25% profit , if cost price for C is 1500 rs , then at how much price did A purchase it ?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick12


Formula

1.
Cost price = (difference
of selling price / difference of profit percent) x 100
2.
Cost price = (difference of selling price / loss% +
profit%) x 100
3.
Cost price =
(difference of selling price / difference of loss percent) x 100
4.
Printed price = (difference
of saving /difference of percentage value ) x 100

Example: If a product is sell at 20% profit instead of 15% profit , then its selling price will become 500 rs , find its cost price?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick13


Formula

The
profit gained on selling a product at X rs , on selling it on Y rs same loss
will be got ,
then cost
price of that product 
= [(X
+ Y) / 2]rs

Example: On selling a watch at 820 rs same profit will be gained that loss is happen on selling it at 650 rs , find cost price of the watch?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick14


Formula

On selling a
product at X rs, profit percent is equal to numerical value of cost price,
then cost
price of that product (or loss%)
= [10 (Root{X+25})  50]rs

Example: On selling a product at 96 rs profit percent will become equal to numerical value of cost price, then find cost price of that product?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick15


Formula

On selling a
product at Y rs instead of X rs , profit will become n times ,
then cost price of that product
= [(nX  Y)
/ (n  1)] rs

Profit , Loss and Discount Type
Profit
, Loss and Discount Trick16


Formula

The profit on selling a product at X rs
is n times of loss on selling that product at Yrs, then cost price of that
product = [(X + nY) / (n + 1)] rs 
Example: The profit on selling a product at 840 rs is double of loss on selling that product at 600 rs , then find the cost price of that product?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick17


Formula

The similar consecutive value of X% and Y%
is – = {(X + Y)  (XY/100)}% or = [1  {1  (X/100)}{1  (Y/100)}] x 100 
Example: What is the similar consecutive value of 10% and 20% ?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick18


Formula

The
three similar consecutive value of X%,Y% and Z% is –
=[1  {1 
(X/100)}{1  (Y/100)}{1  (Z/100)}] x 100

Profit , Loss and Discount Type
Profit
, Loss and Discount Trick19


Formula

After giving the discount of D% , there is
profit of P% , then increase in percent of print rate with respect to
cost price – = [{(P + D) / (100  D)} x 100]% 
Example: A shopkeeper after giving the discount of 20% , earn profit of 20% , then what is increase in percent of print rate with respect to cost price?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick20


Formula

After giving the discount of D1% , there is
profit of P% , then on giving D2%, profit percent will be = [{(100 + P)(100  D2)} / (100  D1) ] 100% 
Example: On giving discount of 10% then profit is 20% , if this discount will be 20% then what will be profit percent?
Profit , Loss and Discount Type
Profit
, Loss and Discount Trick21


Formula

After giving
the discount of D% , there is profit of P% ,
printed
rate of that product will be
= cost price
x [(100 + P) / (100  D)

Example: If a shopkeeper by a product at 3000 rs , what will be print rate so that on giving 25% of discount he will got profit of 10%?
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