Basic Mathematics Form One Notes – Ratio, Profit and Loss
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RATIO, PROFIT AND LOSS
Ratio
A ratio — is a way of comparing quantities measured in the same units
Examples of ratios
1. Acclass has 45 girls and 40 boys. The ratio of number of boys to the number of girls = 40:
45
2. A football ground 100 m long and 50 m wide. The ratio of length to the width = 100: 50
NOTE: Ratios can be simplified like fractions
1 40:45=8:9
2 100: 50=2:1
A Ratio in its Simplest Form
Express a ratio in its simplest form
Example 1
Simplify the following ratios, giving answers as whole numbers
(a) 17:34
(b) 24:14
(0) 56:24
2.4
@) 3’5
3,9
© 58a
Solution
107
(a) Divide by 17 each number 17:34 = 1:2
{b) Multiply by 10 each number 2.4: 1.4= 24:14
Divide by 2 24:14 = 12:7
{) Multiply by 10 each number 5.6: 2.4 = 56:24
Divide by 8 56:24=7:3
(d) Multiply by 9 each fraction == $23 = 6:4
Divide by 2 6:4=3:2
(e) Multiply by 16 each fraction 2 : 2 =6:9
Divide by 3 6:9=2:3
A Given Quantity into Proportional Parts
Divide a given quantity into proportional parts
Example 2
Express the following ratios in the form of
(a) 0.8: 1.6
(b) 55:11
(c) 500 : 250
2.2
@) 3’s
aos
Mig
Solution
108
(a) Divide by 1.6 each number 0.81.6 = es # =05:1
(b) Divide by 11 eachnumber SS: 11= 55: = 5:1
{c) Divide by 250 eachnumber 500: 250 = <2; 2251
250° 250
(d) Multiply by 6 each fraction zibeaed
(e) Multiply by 12 each fraction : : 3 =9:5
Divide by 5 9:5=2: f=18:1
To increase or decrease a certain quantity in a given ratio, multiply the quantity with that ratio
Example 3
a. Increase 6 m in the ratio 4: 3
b. Decrease 800 /— in the ratio 4: 5
Solution
(a) 6m x ‘ =8m
(b) 800/— x 2 = 640/—
Profits and Loss
Profit or Loss
Find profit or loss
If you buy something and then sell it at a higher price, then you have a profit which is given by:
Profit = selling price ~ buying price
If you buy something and then sell it at a lower price, then you have a loss which is given by
Loss = buying price — selling price
The profit or loss can also be expressed as a percentage of buying price as follows:
109
profit
Percentage profit = >” x_ 100%
buying price
And
P r less 100%
c a
ercentage loss = >
Percentage Profit and Percentage Loss
Calculate percentage profit and percentage profit and percentage loss
Example 4
Mr. Richard bought a car for 3, 000, 000/~ and sold for 3, $00, 000’~. What is the profit and
percentage profit obtained?
Solution
Profit= selling price ~ buying price = 3,500,000-3,000,000=500,000
Therefore the profit obtained is 500,000/-
Percentage profit = —Proft 100%
ercontage prof = Face X
But buying price = 3,000,000/— and
Profit = 500, 000/—
s Percentage profit = 990 190% = x 100% = *08% = 16.67%
* Be profit = 5 000,000 “6 mG = 108
Example §
Eradia bought a laptop for
Solution
110
loss
Percentage loss = ————— x_ 100%
buying price
But buying price = 780, 000/~ and loss = buying price — selling price = 780, 000 ~ 720, 000 =
60, 000/-
P tage | £0,000 100% == x 100% = M9 % = 7.60%
ercentage loss = x =a x = 4=
8 780,000 B 13
Simple Interest
Simple Interest
Calculate simple interest
The amount of money charged when a person borrows money e. g from a bank is called interest
0
The amount of money borrowed is called principle (P)
To calculate interest, we use interest rate (R) given as a percentage and is usually taken per year
or per annum (p.a)
| PRT
_ 100
Example 6
Calculate the simple interest charged on the following
a. 850, 000/~ at 15% per annum for 9 months
b. 200, 000/~ at 8% per annum for 2 years
Solution
m
(a) P = 850,000/—, R= 15% T=9 months
Change time from months to years
1 year = 12 months
2? =9 months
_ lyear x 9months _ 9
=” azmonthe 12 97S
9
T=— years
12
9
1 = PRT _ 850,000 x 15 x yy _ 850,000 x 15 x0.75 4.
~ 100 100 ~ 100 ~ /
(b) P= 200,000/-, R=8% T=2years
1 PRT _ 200,000 x8x2_ 4,
~ 100 100 ~ r
Real Life Problems Related to Simple Interest
Solve real life problems related to simple interest
Example 7
Mrs. Mihambo deposited money in CRDB bank for 3 years and 4 months. A t the end of this
time she earned a simple interest of 87, 750/~ at 4.5% per annum. How much had she deposited
in the bank?
Solution
Given I = 87, 750/- R = 4.5% % T= 3 years and 4 months
Change months to years
uz
2 = 4months
= tears imenthe + years = 0:3 years
T= (8+ 03)years = 33years
PRr
1=F8E 001 = pet
100
p= 2001 _ 100 87,750 _ 8775000 _ 55 444
“RT 45×33” 1885 /
She deposited 590 909/—
3