Share this:
RATIO, PROFIT AND LOSS
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
(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
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
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 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/=
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
(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
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
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
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/=
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
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%
(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
B = 70,000 sh
Therefore Buying price = 70,000sh
(b) Solution
Buying price (BP)
Se
lling price (SP) = 30,000/=
lling 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
BP
16%BP = (30,000 – BP) 100%
100%
100%
16BP = 30000 – BP
100 1
4BP = 25(30,000 – BP)
4BP = 25(30,000 – BP)
4BP = 750,000 – 25 BP
4BP + 25BP = 750,000
29BP = 750,000
29 29
BP = 750,000
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
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
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
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%
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:
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/=
Ti
me = 3 years
me = 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:-
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
100
30,000 = 600T
600 600
50 = T
Therefore The time is 50 years
