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

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

Profit = SP – CP                      %P = P/CP * 100                    LOSS = CP –SP             %L = L/CP *100

Example 1: a man buys a pair of shoe for Ħ3000 and sold it for Ħ3300. Find the percentage profit.

Solution:

SP = Ħ3300, CP = Ħ3000,

P = SP – CP = Ħ3300 – Ħ3000 = 300

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

= 10%

Example 2: a market woman bought 50 oranges at a total cost of Ħ2000. She sold each one at Ħ45. Find the percentage profit?

Solution:

CP = Ħ2000, SP =  Ħ 45*  500 = Ħ2250,

P = SP – CP = Ħ2250 – Ħ2000 = Ħ250

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

Ezample 3: A dealer bought an item for Ħ6000 after three months he sold it at a price of Ħ55000. What is the percentage loss?

Solution:

CP = Ħ60000, SP = 55000,

LOSS = CP – SP = Ħ60000 – Ħ55000 = Ħ5000

%LOSS = L/CP  * 100 = 5000/60000  * 100 = 500000/60000

= 8.3%

Example 3:A dealer bought an article for Ħ65000. Find the price he will sell it in order to make a profit of 20%

Solution :

CP = Ħ65000, SP = ?, %P =20%

STEP 1: Find the % of the cost price

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

P = SP – CP = Ħ 13 000 = SP – CP = SP = Ħ 65000 + Ħ 13000 = Ħ 78000

SIMPLE INTEREST

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

Example 1: Mr Smith saves Ħ 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 = Ħ 7000, R = 5%, T = 3

(a). S I = P  *  R  * T/100 = 7000  * 5  * 3/100 – 700  * 15 = Ħ 10000

(b). S I = Ħ70000 * 5 * 7/100 = Ħ 700 * 35 = Ħ 24 500

(C). Ħ70000 * 5 * 5/100 = 700 * Ħ 17500

Amount = P + S I = Ħ 70000 + 17500 = Ħ 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 Ħ5000 per month plus a commission of 15% of all the sales above Ħ100000. Calculate his gross earning in a month if he sells good to the value of Ħ1 200,000.

Solution:

Basis salary = Ħ15000, commission = 15% 0f Ħ100000

But he sold 1200000, therefore Ħ 1200000 –  Ħ100000 = Ħ1100000

15% of 1100000 = Ħ165000

Basic salary + commission = Ħ5000 + Ħ165000 = Ħ180000

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 Ħ84500. How much does he pay?

Solution:

The item cost Ħ84500,12% of 584500

12% of 84500 – Ħ10140

He pays   Ħ84500 – Ħ10140 = Ħ74360.

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 Ħ650000

(b). a Volvo car priced at Ħ450000

(c). a Peugeot car priced at Ħ360000

Solution:

(a). Toyota car = 12.5% of Ħ650000 = Ħ81250

Therefore Ħ650000 – Ħ81250 = Ħ568750

(b). Volvo car = 12.5% of Ħ450000 = Ħ56250

Therefore Ħ450000 – Ħ56250 = Ħ393750

(c).Peugeot car = Ħ12.5% of Ħ360000 = Ħ313500

Ħ360000 – Ħ46500 = Ħ313500

FRACTIONS

HIGHEST COMMON FACTOR AND LOWEST COMMON FACTOR

WHOLE NUMBER AND DECIMALS NUMBERS

SIMPLE EQUATIONS INVOLVING FRACTIONS

MEASURE OF CENTRAL TENDENCY