__B-FACTORY: PROFIT AND LOSS(P&L) - by Rahul Sir__*Let me start by recapitulating the basic concepts that we have studied in school.*

**Cost Price:**The price at which the retailer buys the goods. It is the money the retailer pays.

**Marked Price:**The price at which a good is marked – the printed price

**Selling Price:**The price at which a good is sold. It is the money the customer pays.

**Discount: The difference between MP and SP -> MP-SP=D**

**Profit: The difference between SP and CP -> SP-CP=P**

**Loss: The difference between CP and SP -> CP-SP=L**

**Mark Up: The difference between MP and CP -> MP-CP=M**

**Discount Percentage: D% = D/MP * 100**

**Profit Percentage: P% = P/CP * 100**

**Loss Percentage: L% = L/CP * 100**

**Mark Up Percentage: M% = M/CP * 100**

*The important thing is to be able to view these relations in terms of percentages. This is where most students fail to gain speed. This is where we need to master the art of working with fractions!*

Let me start with the first concept ->

__Value Change:__Let I be the initial value and F the final value. Let p denote the percentage change.

In case of a percentage increase in I:

F = I + I * p/100

ð F = I*(1+p/100)

ð Lets now call this expression p/100 as “f”

ð Let us now call (1+f) as “G”

Now, the relation becomes:

F = I * G

Now, in case of a percentage loss in I => The expression will become

F = I* (1 – f)

ð Let us call (1-f) as “g”

__Percentage Change:__To find the percentage change, we have the following expression:

Percentage Change = (Final Value – Initial Value)/Initial Value * 100

ð %Change = (F-I)/I * 100

ð %Change = (F/I – 1) * 100

Now, with a little bit of understanding, percentage change can also be visualized in terms of fractions.

Let me illustrate this:

F = I(1+f)

ð F/I = 1 + f

ð f = F/I – 1

ð f = p/100

ð p = f*100

ð p = (F/I – 1) * 100

Using these concepts, we can now easily understand the concept of percentages!

Before I take you through the web of P&L Solving => Let me run you through an exercise on fractions.

1. Fractions: Learn this up – this helps!

a. 1/1 = 100%

b. ½ = 50%

c. 1/3 = 33.33%

d. ¼ = 25%

e. 1/5 = 20%

f. 1/6 = 16.67%

g. 1/7 = 14.28571

h. 1/8 = 12.5%

i. 1/9 = 11. 11%

j. 1/10 = 10%

k. 1/11 = 9.09%

l. 1/12 = 8.33%

m. 1/13 = 7.69%

n. 1/14 = 7.14%

o. 1/15 = 6.67%

p. 1/16 = 6.25%

q. 1/17 = 5.882%

r. 1/18 = 5.55%

s. 1/19 = 5.26%

t. 1/20 = 5.00%(-0.26%)

u. 1/21 = 4.76%(-0.24% from previous)

v. 1/22 = 4.54%(-0.22%)

w. 1/23= 4.34%(-0.20%)

x. 1/24 = 4.16%(-0.18%)

y. 1/25 = 4.00%(-0.16%)

z. 1/29 = 3.43%(same pattern as 1/23)

Now, these represent percentages => “f”

Lets work out some values for “G” and “g”:-

Illustration:

10% gain => 1 + 1/10 = 11/10 = G

25% gain => 1 + ¼ = 5/4 = G

66.66% gain => 1 + 2/3 = 5/3 = G

14.28% loss => 1 – 1/7 = 6/7 = g

4.76% loss => 1 – 1/21 = 20/21 = g

Some students find it difficult to find these values fast and quick! So, here is the basic tip

If f= p/q, G = 1 + p/q= (p+q)/q

If f = p/q, g = 1 – p/q = (q-p)/q

So, 1/3rd increase => (1+3)/3 = 4/3

So, 2/5th decrease => (5-2)/5 =3/5

Now, you seem ready for the Profit and Loss Chapter J

**SAMPLE QUESTION 1:**Tarun got 30% concession on the labeled price of an article and sold it for Rs. 8750 with 25% profit on the price he bought. What was the labeled price?

A) 10000 B) 12000 C) 13000 D) 14000

**Solution: M*7/10 *5/4 = 8750**

M = 10000

Lets understand now: M = Marked or the labeled price.

Now, 30% concession on M implies => M *(1-3/10)

Now, this becomes the buying/cost price for Tarun. He now gains 25% => ¼

ð M*(7/10)*(1+1/4)

ð M*7/10*5/4 => the selling price = 8750.

**SAMPLE QUESTION 2:**Ajay bought 15 kg of dal at the rate of Rs 14.50 per kg and 10 kg at the rate of Rs 13 per kg. He mixed the two and sold the mixture at the rate of Rs 15 per kg. What was his total gain in this transaction?

A) Rs 1.10 B) Rs 11 C) Rs 16.50 D) Rs 27.50

**Solution: CP per unit = (15*14.50+10*13)/25 = 13.9**

**SP per unit = 15**

**TOTAL GAIN = 15 – 13.9 = 1.10**

Suppose we had to find out the profit percentage!

**Now, P = f * 100 = (SP/CP – 1) * 100 = (15/13.9 -1)*100 = 7.91%**

Got this one? Let me give you some more examples

**For example, let CP be 2/3 and SP = 5/6**

**P% = (5/6) / 2/3 = (5/4) => 1 + 1/4 => ¼ gain = 25%**

**Hope this helps you visualize P&L as a Percentage Topic!**