Two people X and Y have goats. X has more goats than Y and if Y gives X one of his goats, X will have twice as many goats as Y. If X gives Y one of his goats, they will have an equal number of goats. How goats does each have. (3mks)
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Two grades of coffee one costing sh.42 per kilogram and the other costing sh.47 per kilogram are to be mixed in order to produce a blend worth sh.46 per kilogram in what proportion should they be mixed. (3mks)Worked Answer:John bought 3 brands of tea A, B and C. The cost of the three brands was sh. 25, sh. 30 and sh. 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%.a) How much profit did he make per kilogram of the mixture? (4mks)b) After one year the cost price of each brand was increased by 12%.i) For how much did he sell one kilogram of the mixture to make 20% profit%, give your answer to the nearest 5cts (3mks)ii) What would have been his percentage profit if he sold one kilogram of the mixture at sh. 40.25? (3mks)
Worked Solution:Form 1 Mathematics
Two types of flour, X and Y, cost Ksh60 and Ksh 72 per kilogram respectively.
The two types are mixed such that the cost of a kilogram of the mixture is Ksh 70. Calculate the ratio X:Y of the mixture. Form 1 MathematicsIn a fund raising committee of 45 people, the ratio of men to women is 7: 2. Find the number of women required to join the existing committee so that the ratio of men to women is changed to 5: 4 ( 3 marks) Form 1 Mathematics
A miller was contracted to make porridge flour to support a feeding program. He mixed millet, sorghum, maize and Omena in the ration 1:2:5:1. The cost per kilogram of millet was Ksh 90, sorghum Ksh 120, maize Ksh 30 and omena Ksh 150.
Calculate: (a) the cost of one kilogram of the mixture; (b) the selling price of 1 kg of the mixture if the miller made a 30% profit. Form 1 Mathematics
A trader bought maize for Ksh 20 per kilogram and beans for Ksh 60 per kilogram. She mixed the maize and beans and sold the mixture at Ksh 48 per kilogram. If she made a 60% profit,
determine the ratio maize to beans per kilogram in the mixture. Form 1 Mathematics
a)The ratio of Jumas and Akinyis earning was 5:3. Jumas earnings rose to Kshs 8400 after an increase of 12%
Calculate the percentage increase in Akinyis earnings given that the sum of their new earnings was kshs 14,100. b) Juma and Akinyi contributed all the new earnings to buy maize at Kshs 1175 per bag. The maize was then sold at Kshs 1762.50 per bag. The two shared all the money from the sales of the maize in the ratio of their contributions. Calculate the amount hat Akinyi got. Form 2 Mathematics
A triangular plot ABC is such that the length of the side AB is two thirds that of BC. The ratio of the lengths AB:AC = 4:9 and the angle at B is obtuse.
a) The length of the side BC
b)
i) The area of the plot
iii) The size of ∠ABC Form 1 Mathematics
Three partners Amina, Bosire and Karuri contributed a total of Ksh 4 800 000 in the ratio 4:5:7 to buy an 8 hectares piece of land. The partners set aside 1/4 of the land for social amenities and subdivided the rest into 15 m by 25 m plots.
(a) Find: (i) the amount of money contributed by Karuri; (ii) the number of plots that were obtained. (b) The partners sold the plots at Ksh 50 000 each and spent 30% of the profit realised to pay for administrative costs. They shared the rest of the profit in the ratio of their contributions. (i) Calculate the net profit realised. (ii) Find the difference in the amount of the profit earned by Amina and Bosire. Form 1 Mathematics
Muya had a 6 2/3 ha piece of land. He donated 7/8 ha to a school and 1 1/2 ha to a children's home. The rest of the land was shared equally between his son
and daughter. Find the size of land that each child got. Form 1 MathematicsForm 1 Mathematics
A paint dealer mixes three types of paint A, B and C, in the ratios A:B = 3:4 and B:C = 1:2. The mixture is to contain 168 litres of C.
(a) Find the ratio A:B:C. (b) Find the required number of litres of B. (c) The cost per litre of type A is Ksh 160, type B is Ksh 205 and type C is Ksh 100. i. Calculate the cost per litre of the mixture. ii. Find the percentage profit if the selling price of the mixture is Ksh182 per litre. iii. Find the selling price of a litre of the mixture if the dealer makes a 25% profit. Form 1 Mathematics
A cow is 4 years 8 months older than a heifer. The product of their ages is 8 years. Determine the age of the cow and that of the heifer.
Form 1 Mathematics
A dealer has three grades of coffee X,Y and Z. Grade X costs sh 140 per kg, grade y costs sh 160 per kg grade Z costs sh.256 per kg.
Form 1 Mathematics
Machine A can do a piece of work in 6 hours while machine B can do the same work in 9 hours. Machine A was set to do the piece of work but after 3^{1} ⁄ _{2} hours, it broke down and machine B did the rest of the work. Find how long machine B took to do the rest of the work (3mks)
Form 1 Mathematics
A farmer had 540 bags of maize each having a mass of 112kg. After drying the maize, the mass decreased in the ratio 15:16.
a) Calculate the total mass lost after the maize was dried. b) A trader bought and repacked the dried maize in 90 kg bags. He transported the maize in a lorry which could carry a maximum of 120 bags per trip. i. Determine the number of trips the lorry made. ii. The buying price of a 90 kg bag of maize was Ksh 1,500. The trader paid Ksh 2,500 per trip to the mket. He sold the maize and made a profit of 26 %. Calculate the selling price of each bag of the maize. Form 1 Mathematics
Two alloys, A and B, are each made up of copper, zinc and tin. In alloy A, the ratio of copper to zinc is 3:2 and the ratio of zinc to tin is 3:5.
(a) Determine the ratio, copper: zinc: tin, in alloy A. (b) The mass of alloy A is 250 kg. Alloy B has the same mass as alloy A but the amount of copper is 30% less than that of alloy A. Calculate: (i) the mass of tin in alloy A; (ii) the total mass of zinc and tin in alloy B. (c) Given that the ratio of zinc to tin in alloy B is 3:8, determine the amount of tin in alloy B than in alloy A. Form 1 Mathematics
Bukra had two bags A and B, containing sugar. If he removed 2 kg of sugar from bag A and added it to bag B, the mass of sugar in bag B would be four times the
mass of the sugar in bag A. If he added 10 kg of sugar to the original amount of sugar in each bag, the mass of sugar in bag B would be twice the mass of the sugar in bag A. Calculate the original mass of sugar in each bag. Form 1 Mathematics
Three grades A, B, and C of rice were mixed in the ratio 3:4:5. The cost per kg of each of the grades A, B and C were Ksh 120, Ksh 90 and Ksh 60 respectively.
Calculate: (a) The cost of one kg of the mixture; (b) The selling price of 5 kg of the mixture given that the mixture was sold at 8% profit, Form 1 Mathematics
A trader sells a bag of beans for shs. 2100 and that of maize at shs. 1200. He mixed beans and maize in the ratio 3:2. Find how much the trader should sell a bag of the mixture to realize the same profit.
Form 1 Mathematics
A tea dealer mixes two brands of tea, x and y, to obtain 35 kg of the mixture worth Ksh 62 per kg. 1f brand x is valued at Ksh 68 per kg and brandy at Ksh 53 per kg, calculate the ratio, in its simplest form, in which the brands x and y are mixed.
Form 1 Mathematics
Atieno and Kamau started a business by contributing sh. 25, 000 and sh. 20, 000 Respectively.
At the end of the year, they realized a profit of shs. 81, 000. The profit was allocated to development, dividends and reserves in the ratio 4:5:6 respectively. The dividends were the shared in the ratio of their contribution. Calculate the dividends paid to Atieno. Form 1 Mathematics
Kutu withdrew some money from a bank. He spent 3/8 of the money to pay for Mutua’s school fees and 2/5 to pay for Tatu’s school fees. If he remained with Ksh 12 330, calculate the amount of money he paid for Tatu’s school fees.

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