Ratio:- the ratio of number p and q is p:q or p ÷ q or p/q
Examples:
1. Joha and Siwenza shared 4,000 shillings between them. It Joha received 15,000 shillings and Siwenza got 25,000 shillings,
Find the ratio of the amounts they received:
Solution:
Joha : Siwenza
15,000: 25,000
or
15,000 = 15 = 3
25,000 = 25 = 5
3:5
The ratio of the amount they received is 3:5
2. Express 6:4 in lowest terms
Solution
6 : 4 it can be written as
6/4 = 3/2
6:4 in its lowest term is 3:2
3. Complete the following ratio
(a) 9 : 24 = 3
(b) 15 : 39 = 15
Solution
(a) 9 : 24 = 3
Question:
1. complete the following
(a) 12 : __ = 3 : 7
(b) 4 : 9 = ___ :63
solution
(a) 12 : __ = 3 : 7
(b) 4 : 9 = ___ :63
solution
4 : 9 = ___ : 63
Proportions
1. Divide 120 shillings the ratio 3 : 7
Solution
3 + 7 = 10
3 x 120 = 36 shs
10
7 x 120 = 84 shs
10
Therefore 3 of 120 is 36 shs
10
7 of 120 is 84 shs
10
2. divide 156 in the ratio of 3 : 4 : 5
solution
3 : 4 : 5
3 + 4 + 5 = 12
+ 7 = 10
3 x 156 = 39
12
3 of 156 is 39
12
4 x 156 = 52
12
4 of 156 is 52
12
5 x 156 = 65
12
5 of 156 is 65
12
Question
1. Juma, Ali, Mary and Kalo have 300, 100, 500 and 600 shaves in a cooperative shop respectively. Divide 150,000 shs among them in the ratio of their shaves
Solution
300, 100, 500 and 600
= 300 + : 100 + : 500 + : 600
= 3: 1: 5: 6
= 3: 1 : 5: 6
= 3 + 1 + 5 + 6 = 15
= 3 x 150,000 ÷ 30,000
15
= Juma hot 30,000 shs
1/15 x 150,000 = 10,000
Ally got 10,000 shs
5/15 x 150,000 = 30,000
Mary gor 50,000 shs
6/15 x 150,000 = 60,000
Kalo got 60,000 shs
Profit and loss
Profit = Selling price – buying price
Loss = Buying price – selling price
Percentage profit = profit made x 100%
buying price
Percentage loss = loss made x 100%
buying price
Example:-
1. A ration is bought for 24,000 shs and sold for 36,000 shs. Find
(a) The profit made
(b) The percent profit
Solution
(a) Buying price = 24,000/=
Selling price = 36,000/=
The profit made
= Selling price – buying price
= 36,000/= – 24,000/=
= 12,000/=
(b) The percentage profit
= profit made x 100%
Buying price
= 12,000 x 100%
24,000
= ½ x 100%
= 50%
2. A dealer paid 800,000/=for a machine and solid it the following year for 600,000/=
Find: (a) the loss made
(b) the percentage loss
(a) Solution
The loss made
= Buying price – selling price
Buying price = 800,000/=
Selling price = 600,000/=
800,000 – 600,000
= 200,000/=
(b) Solution
Loss made = 200,000/=
Buying price =800,000/=
The percentage loss
= loss made x 100%
Buying price
=200,000 x 100%
800,000
= 1 x 100%
4
= 25%
Question
1.A house was sold a profit of 900,000. If its late of the profit is 37 1/2. Find the lost (buying price) of the house
Solution
Profit made = 900,000
The percentage profit = 37 1/2
Buying price = ?
profit made x 100%
Buying price
37 1/2 = 900,000 x 100%
1 buying price
B = 900,000 x 100%
37 1/2
= 900,00 x 100
75/2
= 900,000 x 2
1 75
= 180000000
75
= 2,400,000/=
2. A dealer paid sh. 20,000 for 10 books. He sold 2/5 of them at 3000 each and the remaining at 2500 each. What was his percentage profit?
Solution
2/5 x 10 = 4
4 x 3,000 = 12,000 shs.
1/3 – 2/5 = 3/5
3/5 x 10 = 6
6 x 2500 = 15,000 shs
12,000shs + 15,000 shs
= 27,000 shs
Profit = Selling – Buying piece
= 27,000 shs – 20,000 shs
= 7,000 shs.
Percentage profit = Profit made
Buying price
7,000 x 100%
20,000
= 7000
200
= 35 %
Percentage is 35%
Question
1.Find the profit or loss when an article bought for
(a) 4000 sh and sold at 48000/=
(b) Sh. 1250 and sold at 1500/=
Solutions
(a) The profit made = Selling price – buying price
buying price = sh 4000
selling price = sh 4800
profit = selling – buying
= sh 4800 – 4000
= sh 800
(b) buying price = 1250sh
selling price = sh 1500
profit = selling – buying
profit = sh 1500 – sh 1250
= 250 sh
(c) buying price = 2000sh
selling price =1400sh
loss = buying – selling
= 2000sh – 1400sh
= 600sh
2. Find the buying price of an article which is sold at:-
(a) 98000sh at a profit of 40%
(b) 30,000 sh at profit of 16%
(c) 108,500 sh at profit of 7%
(a) Solution
Buying price = ?
Selling price = 98000 sh
Percentage profit = 40%
But percentage profit
= Profit made x 100%
Buying price
40% = Profit made x 100%
Buying price
40% = profit made
100 Buying price
But profit made = S. P – B .P
2/5 = Selling – Buying
Business price
2/5 = 98000 – B
B
2 X B = 5 ( 98000 – B)
2B = 490000 – 5B
2B + 5B = 490,000
7B = 490,000
7 7B
B = 70,000 sh
Therefore Buying price = 70,000sh
(b) Solution
Buying price (BP)
Selling price (SP) = 30,000/=
Percentage profit (PP) = 16%
PP = PM X 100%
BP
PM = SP – BP
16% = (SP – BP )100%
BP
BP X 16% = (30,000 – BP X 100%)BP
BP
16%BP = (30,000 – BP) 100%
100%
16BP = 30000 – BP
100 1
4BP = 25(30,000 – BP)
4BP = 750,000 – 25 BP
4BP + 25BP = 750,000
29BP = 750,000
29 29
BP = 750,000
29
BP = 25862.7
Therefore the buying price of an article is 25862.07shs
(c) 108,500 sh at profit of 7%
Data given :
selling price = 108,500sh
profit percentage = 7%
buying price = ?
But the percentage profit = profit made x 100%
buying price
7% = profit made
100% buying price
But the profit made
= selling price – buying price
7 = selling price – buying price
100 buying price
7 = 108,000 – B
100 B
7 x B = 100(108,500 – B)
7B = 108,500 – 100B
100B + 7B = 108,500
107B = 108,500
107 107
B = 10140.19sh
Therefore The buying price of an article is 10140.19sh
3. find the article which is bought for 25,000 sh and sold at profit of 24%
solution
Data given ;
Buying price = 25,000sh
profit percentage = 24%
selling price = ?
but profit percentage
profit made x 100%
buying price
24% = profit made x 100%
buying price
24 = profit made
100% buying price
But profit made
= selling price – buying
6 = selling price – buying price
25 buying price
6 = S.P – 25,000
25 25,000
6 X 25,000 = 25 (S.P – 25,000)
150,000 = 25S.P – 625,000
625,000 + 150,000 = 25S.P
775,000 = 25S.P
25 25
31,000 = S.P
Therefore Selling price of the article is 31,000 sh
4. A machine losting 18000/= is sold at profit of 40%. What is the selling price?
solution
Data given :
buying price = 180,000
profit percentage = 40%
selling price = ?
40 x 180,000
100
= 40 x 1,800
= 72,000 sh
Then 180,000 sh + 72,000 sh
= 252,000 sh
Therefore Selling price of machine is 252,000 sh
5. At a clearance sale boots which are cost 30,000 sh each were sold at a loss of 25%. Calculate the loss and clearance price
Solution
Data given :
buying price = 30,000
loss = 25%
loss made = 25% x 30,000sh
= 25 x 30,000sh
100
= 7,500 sh
The loss made of boots is 7,500 sh
Clearance price (selling price)
loss made = buying – selling price
7,500sh = 30,000sh – S
7,500 – 30,00 = – S
-22,500 = -S
-1 -1
Therefore Clearance price is 22,500sh
SIMPLE INTEREST
- Simple interest (1): Is the amount of money paid as a profit.
- Principle (P): The money borrowed or deposited or lent.
- Rate (R) : Is the principle change per year.
- Time (T): Period I year
- Amount (A): The sum of principle and interest
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Interest = Principle x made x Time
100
I = PRT
100
Examples:
- Find the simple interest on 18,000 sh for 2 year at rate of 6%
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Solution
Data given:
Principle = 18,000 sh
Rate = 6%
Time = 2 years
Interest = ?
I = PRT
100
I = 18,000 x 6 x 2
100
I = 180 X 12
= 2,160
Therefore the simple interest is 2,160 sh
Solution:
Data given:
Simple interest = 90,000 sh
Rate = 4 %
Time = 5 years
Principle =?
I = PRT
100
90,000 = P x 4 x 5
100
90,000 = 20P
1 100
20P x 1 = 90,000 x 100
20 20
P = 450,000 SH
The principle is 450,000 sh.
EXERCISE
1. Find the percentage rate at which interest on :
(a) 20,000 /= for 4 years is 2000/=
Solution
Data given:
Interest = 2000/=
Principle = 20,000/=
Time = 4 years
Rate = ?
I = PRT
100
20,000 = 200 x R x 4
100
20,000 = 800 R
800 800
25 % = R
:. Rate is 25%
(b) 16, 0000 /= for 3 years is 9600/=
Solution
Data given
Interest = 96, 00/=
Principle = 160,000/=
Time = 3 years
Rate =?
I = PRT
100
9600 = 160,000 x R x 3
100
9600 = 4800 R
4800 4800
2% = R
:. The rate is 2%
2. Find the principle that would earn 54,000 /= in 10 years at rate of 5%
Solution
Data given
Interest = 54,000/=
Rate = 5%
Time = 10years
Principle = ?
I = PRT
100
54,000 = P x R 10
2100
54000 = P x 2
2
108000 = P
:. The rate principle is 108 ,000/=
1. Find the simple interest on 54,000/= inverted for 18 months at the rate of 12% per annum
Solution
Data given
Interest =?
Principle = 54,000/=
Rate = 12
Time = 18 months
= 1 years and 6 months
= 1 years and half
I = PRT
100
54,000 x 12 x 1 ½
100
540 x 6 x
= 3,240 =
:. The simple interest is 3.240 /=
EXERCISE 2
1. Find the simple interest on
(a) 80,000 sh for 1 year at rate of 20% per annum
Solution
Data given:
Principle = 80,000/=
Rate = 20%
Time = 1 year
Interest = ?
But, I = PRT
100
I = 80,000 x 20 x 1
100
= 800 X 20
= 16,000
The simple interest is 1,600/=
(a) 14,000/= for 1 year at rate of 3% per annul
Solution:-
Data given:
Principle = 14,000/=
Rate = 3%
Interest = 1 year
But, I = PRT
100
I = 14,000 x 3 x 1
100
= 140 x 3
= 420/=
The simple interest is 420/=
2. Find the number of year (time in year ) in which the interest on:
(a) 20,000/= at the rate of 4% is 4,800/=
Solution:
Data given:
Principle = 20,000/=
Rate = 4%
Interest = 4,800/=
But, I = PRT
100
4,800 = 20,000 x 4 x I
100
4,800 = 800T
800 800
6 = T
The time is 6 years
(b) 50,000/= at the rate of 1% in 30,000/=
Solution:
Data given:
Principle = 60,000/=
Rate = 1%
Interest = 30,000
But, I = PRT
100
30,000 = 60,000 X 1 X T
100
30,000 = 600T
600 600
50 = T
Therefore The time is 50 years
