## HOUSEHOLD ARITHMETIC (SIMPLE INTEREST, PROFIT AND LOSS, DISCOUNT AND COMMISSION)

**PROFIT AND LOSS**

When a trader buys or sells goods, the price at which he /she sells is called *selling price* while the price at which he/she buys is called *cost price*.

When the good is sold at a price greater than the cost price, then the trader has made a ** gain **or

**On the other hand, when the good is sold at a price less than the cost price, then the trader has made a**

*profit.*

*loss.*S.P means selling price, C.P means cost price.

*Profit = SP â€“ CPÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â %P = P/CP * 100Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â LOSS = CP â€“SPÂ Â Â Â Â Â Â Â Â Â Â Â %L = L/CP *100*

Example 1: a man buys a pair of shoe for Ä¦3000 and sold it for Ä¦3300. Find the percentage profit.

Solution:

SP = Ä¦3300, CP = Ä¦3000,

P = SP â€“ CP = Ä¦3300 â€“ Ä¦3000 = 300

%P = P/CPÂ * 100 = 300/3000 * 100 = 30000/3000

= 10%

Example 2: a **market** woman bought 50 oranges at a total cost of Ä¦2000. She sold each one at Ä¦45. Find the percentage profit?

Solution:

CP = Ä¦2000, SP =Â Ä¦ 45*Â 500 = Ä¦2250,

P = SP â€“ CP = Ä¦2250 â€“ Ä¦2000 = Ä¦250

SP = P/CP * 100 = 250/2000 * 100 = 25000/2000 = 12.5%

Ezample 3: A dealer bought an item for Ä¦6000 after three months he sold it at a price of Ä¦55000. What is the percentage loss?

Solution:

CP = Ä¦60000, SP = 55000,

LOSS = CP â€“ SP = Ä¦60000 â€“ Ä¦55000 = Ä¦5000

%LOSS = L/CPÂ * 100 = 5000/60000Â * 100 = 500000/60000

= 8.3%

Example 3:A dealer bought an article for Ä¦65000. Find the price he will sell it in order to make a profit of 20%

Solution :

CP = Ä¦65000, SP = ?, %P =20%

STEP 1: Find the % of the cost price

P = 20/100Â Â * 65000 = 130000/100 = 13000

**P = SP â€“ CP = Ä¦ 13Â 000 = SP â€“ CP = SP = Ä¦ 65000 + Ä¦ 13000 = Ä¦ 78000**

**SIMPLE INTEREST**

SI = P * RÂ * T/100 where PÂ principal, R = rate, T = time and SI = simple interest

Example 1: Mr Smith saves Ä¦ 70000 with a bank for 3 years at the rate of 5%.

(a). calculate the interest he will receive at the end of the years

(b). calculate the simple interest for 7 years

(c). what is the total amount he will save at the end of 5 years?

Solution:

P = Ä¦ 7000, R = 5%, T = 3

(a). S I = PÂ *Â RÂ * T/100 = 7000Â * 5Â * 3/100 â€“ 700Â * 15 = Ä¦ 10000

(b). S I = Ä¦70000 * 5 * 7/100 = Ä¦ 700 * 35 = Ä¦ 24Â 500

(C). Ä¦70000 * 5 * 5/100 = 700 * Ä¦ 17500

Amount = P + S I = Ä¦ 70000 + 17500 = Ä¦ 87500

**COMMISSION AND DISCOUNT**

**Commission** is simply a payment received for selling a good.

Example 1: An insurance company pays an agent a basis salary of Ä¦5000 per month plus a commission of 15% of all the sales above Ä¦100000. Calculate his gross earning in a month if he sells good to the **value** of Ä¦1 200,000.

Solution:

Basis salary = Ä¦15000, commission = 15% 0f Ä¦100000

But he sold 1200000, therefore Ä¦ 1200000 –Â Ä¦100000 = Ä¦1100000

15% of 1100000 = Ä¦165000

Basic salary + commission = Ä¦5000 + Ä¦165000 = Ä¦180000

**DISCOUNT **is the amount of **money** taken of a price of a good in order to promote the sale.

Example: Mr adeoye, a regular customer is given a discount of 12% on an item that cost Ä¦84500. How much does he pay?

Solution:

The item cost Ä¦84500,12% of 584500

12% of 84500 â€“ Ä¦10140

He paysÂ Â Ä¦84500 â€“ Ä¦10140 = Ä¦74360.

Example 2: A car company advertises a discount of 12.5% of all their vehicles. How much would it cost to purchase.

(a). a Toyota car priced at Ä¦650000

(b). a Volvo car priced at Ä¦450000

(c). a Peugeot car priced at Ä¦360000

Solution:

(a). Toyota car = 12.5% of Ä¦650000 = Ä¦81250

Therefore Ä¦650000 â€“ Ä¦81250 = Ä¦568750

(b). Volvo car = 12.5% of Ä¦450000 = Ä¦56250

Therefore Ä¦450000 â€“ Ä¦56250 = Ä¦393750

(c).Peugeot car = Ä¦12.5% of Ä¦360000 = Ä¦313500

Ä¦360000 â€“ Ä¦46500 = Ä¦313500

See also

HIGHEST COMMON FACTOR AND LOWEST COMMON FACTOR

WHOLE NUMBER AND DECIMALS NUMBERS

SIMPLE EQUATIONS INVOLVING FRACTIONS