## Questions

- Three business partners Georgina, Gilbert and Akumu decided to buy a plot worth shs.510,000. They contributed shs.30000; as a deposit in the ratio 2:3:5 respectively.

They paid the balance in two months by contributing equal amounts. After one year, they sold the plot for a profit of 20% and invested the initial capital in another business.

The profit was shared in the ratio 1:2:3; respectively. Find how much each partner- contributed towards the deposit
- paid to clear the balance
- received as a profit

- Twelve men take 20 days to complete a piece of work. How long would 16 men take to do the same piece of work?
- Mr. Kitur bought grades of tea ; Grade A costs shs.109 per kg and a kg of Grade B costs shs.81.50. In what ratio must he mix the two grades in order to make a profit of 20% by selling the mixture at Kshs.112.80per kg?
- Mogutu and Onacha working together can do a piece of work in 6days. Mogutu working

alone takes 5days longer than Onacha. How many days does it take Onacha to do the work alone? - Given the curve y = 2x3 + ½x2 – 4x + 1, find the equation of the normal to the curve at (1, -½)
- A and B are connected by the equation B = KA + M where K and M are constants.

The table below shows the values of A and corresponding values of B

A 1.5 3.0 4.5 6.0 7.5 B 8 11 14 17 20 - Draw a suitable straight line on the grid provided
- State the values of K and M, hence express B in terms of A

- The latitude and longitude of two stations P and Q are (47
^{o}N, 25^{o}W) and (47^{o}N, 70^{o}W) respectively. Calculate the distance in nautical miles between P and Q along the latitude 47^{o}N - A coffee blender mixes 6 parts of types A with 4 parts of type B. If type A costs Kshs. 72 and type B costs him Ksh.66 per kg respectively at what price should he sell the mixture in order to make a profit of 5%. Give your answer to the nearest ten cent.
- Paint A costs shs.150 per litre while B costs shs.160 per litre. In what proportion must A be mixed with B to produce a mixture costing shs.156 per litre
- What must be the selling price of the mixture if a profit of 12% is to be realized?

- A cylindrical water tank can be filled to a depth of 2.1m by a pipe P in 2 hours. Pipe Q takes 7 hours to fill the tank to the same level. Pipe R can empty this

amount of water in 6hours. Initially, the tank is empty. Pipes P and Q are turned on at 8.45a.m and pipe R at 9.45a.m. Find the depth of water in the tank at 11.45a.m

- Two grades of tea leaves one costing sh.420 per kilogram and the other costing sh. 470 per kilogram are to be mixed in order to produce a blend worth sh.455 per kilogram. In what proportion should they be mixed?
- The internal radius of a pipe is 0.35m. Water flows through the pipe at the rate of 45cm per second. Calculate the amount of water that passes through the pipe in 2 ¼ hours in litres
- In 2000 the total cost of manufacturing an item was ksh1250 and this was divided among the costs of material, labour and transport in the ratio of 8:14:13. In 2003 the cost of material

was doubled, labour cost increased by30% and transport costs increased by 20%- Calculate the cost of manufacturing this item in 2003
- In 2004 the cost of manufacturing the same item was ksh1981 as a result of increase in labour costs only. Find the percentage increase in labour costs of 2004

- Brand A tea costing Kshs.80 per kg is mixed with Brand B tea costing Kshs.100 per kg such that the mixture is sold at Kshs.114 making a profit of 20%. Find the ratio of A:B
- In what proportion must teas of Kshs.76 and Kshs.84 per kg be mixed to produce a tea costing Kshs.81 per kg
- Onyango bought 3 brands of tea P, Q and R. the cost price of the three brands were shs.25, shs.30 and shs.45 per kilogram respectively. He mixed the three brands in the

ratio 5:2:1 respectively After selling the mixture, he made a profit of 20%- How much, profit did he make per kilogram of the mixture?
- After one year, the cost price each brand was increased by 12%.
- For how much did he sell one kilogram of the mixture to maintain 20% profit. Give your answers to the nearest 5cts.
- What would have been his percentage profit if he sold one kilogram of the mixture at shs.40.25?

- A mixture contains two powders X and Y with masses in the ratio 3:11. If the mixtures Cost Shs.6.70 per kg and powder x costs Shs.5.60 per kg. Find the cost of 1kg of powder Y

## Answers

- Deposit: Total ratio 2 + 3 + 5 = 10

Georgina:^{2}/_{10 }x 30000 = 6000

Gilbert:^{3}/_{10 }x 30000 = 9000

Akumu:^{5}/_{10 }x 30000 = 15000 - Balance to be paid

= 510000 – 30000 = 480000

Each pays = 480000 = 160000

3 - Profit =
^{20}/_{100 }x 510000 = 102000

Georgina received:^{1}/_{6}x 102000= 17000

Gilbert received:^{2}/_{6}x 102000 = 34000

Akumu received:^{3}/_{6 }x 102000 = 51000

- Deposit: Total ratio 2 + 3 + 5 = 10
- Men Days

12 20

16 ?

= (12 x 20) days

16 = 15 days -

Cost of mixture

Sh 112.8 x 100 = 94 per kg

120

Ratio A : B

(81.50 – 94) : (109 – 94)

12.5 : 15

2.5 : 3

5 : 6

Alt. At selling Price

A sales at 109 x 120

100

= 130.50/=

B sales at 81.50 x 120

100

= 97.80/=

A & B mixed sells at

94 x 120 = sh 112.80 per kg

100

Ratio A : B

(112.80 – 97.8) : (130 – 112.8)

15: 18

5 : 6 - Let Onacha take x days.

Mogutu takes x + 5 days.

1 + 1 = 1

x x + 5 6

x^{2 }(x + 5) + 6x = x(x – 5)

x^{2}–x – 30 = 0

(x – 10) (x + 3)

x = 10, 3 Onacha takes 10 days. ^{dy}/_{dx }= 6x^{2}+ x – 4

When x = 1,^{dy}/_{dx }= 6+1 -4 = 3

Grad of normal = -^{1}/_{3}y + ½ = -^{1}/_{3}(x - 1)

y=-^{1}/_{3}x –^{1}/_{6}_{}Gradient = 11 – 8

3 – 1.5

= 2

K = 2, M = 5 B = 2A + 5- (70 – 25 x 60 = 2700

2700 Cos 47

= 2700 x 0.68 = 1841.4nm - 6 x 72 + 66 x 4 = 69.6

10

100% = 69.6

∴ 105 = 73.10 - A B Mixture

150 160 156

1 n 1+n

150 160n (n+1)156

150 + 160n = 156(n+1)

N =^{6}/_{4 }=^{3}/_{2}= 112 x 156 = shs. 174.72

100

- A B Mixture
- At 11.45 a.m

Depth filled by P in 2hrs = 2.1m

3hrs = 3hr x 2.1m

2hr

= 3.15m

Depth filled by q in 7hrs = 2.1m

3hrs = 3hrs x 2.1m

7hrs

= 0.9m

Depth emptied by R in 6hrs = 2.1m

2hrs = 2hr x 2.1

6hrs

∴ Depth at 11.45a.m = (3.15 + 0.9) – 0.7 = 3.35m

- Let the amount to be mixed be x kg of the lower, priced grade and y kg for higher price grade

X kg of the lower priced grade cost Sh. 420x

Y kg of the higher priced grade cost Sh.470y

Total cost of (x+y) kg of mixture

= Shs. 420 x + 470y

x + y

equating 420x + 470y = 455

x + y

420 x + 470y = 455x + 455y

470y – 455y = 455x – 420y

15y = 35x

X: y = 3:7 - Cross sectional area = r
^{2}= (22 x 35 x 35)cm^{2}

7

Flow per second = (22 x 35 x 35 x 45)cm^{2}

7

After 2¼ hrs = (22 x 35 x 35 x 45 x 3 x 60 x 69)liters

7

= 233887.5litres - In 2000, Costs Shs

Material = 8/25 x 1250 = 400

Labour = 14/25 x 1250 = 700

Transport = 3/25 x 1250 = 150

In 2003

Material = 400 x 2 = 800

Labour = 130/100 x 700 = 910

Transport =120/100 x 150 = 180 - In 2004 Costs

Material = 800

Transport = 180

∴ labour = 1981 – (800 + 180)= Shs.1001

∴ Increase in labour = 1001 – 910 = 91

% increase =^{91}/_{910 }x 100

= 10%

- In 2000, Costs Shs
- Cost price = 100 x 114 = shs. 95

120

Let A: B = n :1

95 = 80n + 100

1 n + 1

95n + 95 = 80n + 100

15 n = 5

n =^{1}/_{3}n:1 =1:3

A:B = 1:3 - Let the ratio be x: y

76x + 84y = 81(x + y)

84y – 81y = 81x – 76x

3y = 5x

3 = x

5 y

x : y = 3 : 5 - Cost of 8kg = 5 x 25 + 2 x 30 + 1 x 45 = 230

Cost of 1 kg= 230/8 = 28.75

Profit/ kg= 28.75 X 20/100

= 5.75 - Selling price

= 28.75 x^{112}/_{100 }= 32.20

32.20 x^{120}/_{100 }= 38.64

38.64 - New cost/ kg

= 1.12 x 28.75 = 32.20

% Profit = 40.25 – 32.20 X 100

32.20

= 25%

- Selling price

- Cost of 8kg = 5 x 25 + 2 x 30 + 1 x 45 = 230
- = 3(5.60) + 11y = 6.70

14

= 16.8 + 11y = 93.8

11y = 77

y = 7

1Kg costs Shs. 7.00

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