**GETTING STARTED**

This topic is a **pure application of Unitary method**. Every trader does business in order to make profits.

**☛ ** The cost at which he buys goods is known as **‘Cost Price’**. If he is making a product with raw materials purchased, **all the cost incurred in making the final product is ‘cost Price’ (C.P)**.

**☛ **The price at which he sells the product is known as **‘Selling Price’ (S.P)**.

**☛ **In transactions where

** S.P > C.P , he makes ‘profit’**

**☛ **Transactions where

** C.P > S.P, he makes ‘loss’**.

**☛ Profit = S.P – C.P**

**☛ Loss = C.P – S.P**

**Eg. A trader buys cups from a manufacturer at Rs. 100 and sold it for Rs. 120 to his customer. Did he gain or lose in this transaction?**

Here, CP = Rs.100

S.P = Rs. 120

S.P > C.P. Therefore the trader has made a profit.

**Profit = Rs. 120 – Rs.100 **

** = Rs. 20**

**☛ Profit % and Loss % are always calculated by taking C.P as the base.**

**Profit % = Profit /C.P x 100**

**Loss % = Loss/C.P x 100**

In the previous example, the profit was Rs. 20 on a base (investment) of Rs.100.

**Profit % = 20/100x 100 = 20%**

Depending on outcome of the transaction,

**S.P = C.P + Profit** or

**S.P = C.P – Loss**

**Eg. A vegetable seller bought vegetables for Rs. 1800 from the market. After selling all the vegetables, he was left with Rs. 700 profit. Calculate the S.P**

Soln:

C.P = Rs. 1800.

Profit = Rs. 700

S.P = Profit + C.P

= Rs. 1800+ Rs.700

=**Rs. 2500**

**Finding S.P with Profit/ Loss % and C.P**

Many a times, we may have only Profit % and Cost Price, with which we may have to find the Selling Price.

**Eg. Let us say, a man makes profit of 5% on C.P of Rs. 1200. What is the selling price? **

Soln:

As we know, profit is always calculated with CP as the base.

If the **profit is 5%, it means that, for a C.P of every Rs. 100, he makes Rs. 5 profit.**

Thus for every Rs. **100 as C.P, Rs. 105 is S.P**

When C.P is Rs. 1200, What will be S.P? – **Application of Unitary method**

Hence,** S.P = 1200/100*105 **

**= Rs. 1260**

**Eg. ****Let us say a man made a loss of 20% on articles bought for Rs. 1500. What would the selling price?**

** **Soln:

Applying a similar approach as above, for a **C.P of Rs. 100, man made a loss of Rs. 20.**

S.P = Rs. 80 when C.P= Rs. 100

When C.P = Rs.1500,

S.P = 80/100 X 1500

= **Rs.1200**

**Discount Problems**

When we go to a shop, discount is one thing everyone keeps looking for.

It is nothing but the **difference between** the **price originally quoted by shopkeeper (Marked Price)** and the **final price you buy it for (Selling Price)**.

** ☛ Discount **

** = Marked Price – Selling price**

**Discount is always applied considering Marked Price as the base. **

☛**Discount%**

** =Discount/Marked Price x 100**

**Eg.** If a product’s Marked Price is Rs.200 and 30% is the discount given, then the object is sold for Rs.30 discount.

Discount = 30 / 200 x 100

Hence, **Discount = Rs. 60**

**Thus, Product was sold for Rs.140**

**Eg. ****A shopkeeper gave a discount of 10% but still managed to make a profit of 20% over Cost Price of Rs. 3000. What was the marked price of the product?**

** Soln:**

The cost price of product is **Rs. 3000.**

** Profit % = 20%**

**Profit = 20/100 x 3000 = Rs. 600**

**S.P = Rs. 3000+ Rs.600 **

**= Rs.3600**

**Discount % = 10 %**

It means that if the marked price is Rs. 100, the discount is Rs. 10 and the Selling price is Rs. 90.

Here SP = Rs.3600, therefore,

C.P = 3600/90 x 100

= **Rs. 4000.**

# PARTNERSHIP

**GETTING STARTED**

People invest in business to make profits. When two or more people invest in a business, it is known as ‘Partnership’.

Whenever a profit is made by a business, amount invested and duration for which the amount was invested dictates the ratio in which profit is shared by the partners.

Profit ( directly proportional ) Investment

Profit (directly proportional) Time for which investment is done.

Therefore,

** _{ }**P

_{1 }– Profit by 1st Person

I_{1} – Investment by 1st person

T_{1}– Time for which money was invested by 1st person

P_{2 }– Profit by 2nd Person

I_{2 }– Investment by 2nd person

T_{2 }–_{ }Time for which money was invested by 1st person

**Eg. A and B entered into a partnership where A invested Ra.300 for first 3 months and Rs. 600 for next 9 months. On the other hand, B invested Rs.500 for the entire year. In what ratio will their profit of Rs. 820 be divided?**

**Soln:.**

**P _{1}/P_{2 } **

**= ((300×3)+(60×9))/(500×12)**

= 6300/6000

= 21/20

If the profit was Rs.41, **A would receive Rs. 21 and B would receive Rs.20**.

When profit is Rs.820, **A will receive 820/41 x 21 = Rs. 420 and B will receive Rs. 400.**