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## 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

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