MATHEMATICS FORM 1 – RATIO, PROFIT AND LOSS

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

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

1. Simple interest (1): Is the amount of money paid as a profit.
2. Principle (P): The money borrowed or deposited or lent.
3. Rate (R) : Is the principle change per year.
4. Time (T): Period I year
5. Amount (A): The sum of principle and interest

Interest = Principle x made x Time

100

I = PRT

100

Examples:

1. 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:

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