# Profit and Loss quantitative aptitude concept and questions

Cost Price(CP)-The price at which an article is purchased is called its cost price.
Selling Price(SP)-The Price at which an article is sold is called Selling Price.

##### Condition 1

When SP > CP
then Profit occurs and Profit= SP – CP

##### Condition 2

When CP > SP
then Loss occurs and Loss= CP – SP

Intext Question
Suppose if Shyam goes to market and buys a mobile phone at Rs 5000. So, CP is Rs 5000. A few days later he wanted to buy a new phone because that phone did not support Whatsapp.He decides to sell that phone to his friend at Rs 4000.The Selling Price or SP is Rs 4000.

CP of phone= Rs 5000
SP of phone= Rs 4000
Here, CP > SP(CP is greater than SP)
Loss occurs and Loss = CP – SP
= 5000-4000= Rs 1000

After Knowing Profit and Loss Let us find Gain Percent and Loss Percent

#### Formulae

• $Gain\%=\frac{Gain}{CP}\times100$
• $Loss\%=\frac{Loss}{CP}\times100$

Note-We can simply remember these formulae , Just divide Gain or Loss with CP and multiply with 100 to get Gain % or Loss %

In the above problem, Loss % =(Loss/CP)*100 = (1000/5000)*100=20%

#### Some More Formulae

To find SP when CP and gain% or loss% is given

• $SP=\frac{100+R}{100}\times CP$ where R is gain %
• $SP=\frac{100-R}{100}\times CP$ where R is loss %

To find CP from SP and gain% or loss% is given

• CP={100/(100+R)}*SP where R is gain %
• CP={100/(100-R)}*SP where R is loss %

Quick tip-
If an article is bought at Rs 100 and sold at 20% gain then SP is equal to 120% of Rs 100 i.e Rs 120.
SP=(100+R)% of CP (Here of means multiplication)
Similarly if it is sold at 20% loss, SP is equla to Rs 80.
SP=(100-R)% of CP

If We simply re-express this formula
CP={SP/(100+R)%} if R is gain %
CP={SP/(100-R)%} if R is loss %

#### Short tricks:-

• If a seller sells two article one at say x% loss and other at x% gain, he will always have a loss.
$Loss\%=\left [ \frac{x}{10}\right ]^{2}$
• If a person sells article at the cost price but use false weight
$Gain\%=\frac{Error}{(true value-error)}\times 100$
Important Formulae To Remember
• $Gain\%=\frac{Gain}{CP}\times100$

• $Loss\%=\frac{Loss}{CP}\times100$

• $SP=\frac{100+R}{100}\times CP$ where R is gain %

• $SP=\frac{100-R}{100}\times CP$ where R is Loss %

• $CP=\frac{100}{100+R}\times SP$ where R is gain %

• $CP=\frac{100}{100-R}\times SP$ where R is gain %
Intext Questions
1.
a)Find gain or loss percent if SP=500 and CP=800.
Here CP>SP so, loss%=(CP-SP)/CP * 100=(300/800)*100=75/2 %

b) Find SP if CP is 500 and gain % is 20%
SP=(100+R) % of CP = (120*500)/100=600

c) Find CP if SP is 500 and loss is 30%
CP= 500/70% = (500*100)/70

2.By selling an article for Rs 1200 a person makes 20% profit.What is gain or loss % if he sells it for Rs 1500.
Ans- Here CP=(1200/120)*100=1000
gain%={(1500-1200)/(1200)}*100=25%

3.A dishonest man sells his goods at the cost price, but he uses a weight of 960 grams for 1 kg.Find his gain %
Ans Using trick:-
Error = Real weight- false weight=40gm
gain%={Error/(true wt- error)}*100 ={40/(1000-40)}*100=40/960 *100 = (25/6)%

4.If CP of 21 article is equal to SP of 18 article .Find gain or loss percent.
Ans- in this type of problem consider CP of aricle be Rs 1.
CP of 21 article = SP of 18 article
SP of 1article=(21/18)
gain% = {(21-18)/18}*100

Profit and Loss quantitative aptitude is generally asked in all major exams like IBPS,GATE,CAT.It is very necessary to understand the profit and Loss quantitative aptitude concept and questions should be practiced accordingly.I think this chapter will help you in the competitive exams.