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Form 3 Mathematics Compound Proportions and Rates of Work Questions and Answers
Given that the ratio x:y = 2:3, find the ratio (5x2y) : (x+y)
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1.
Aden bought 3 brand of tea A,B and C. The cost price of the three brands were 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 b) After one year,the cost price of each brand was increased by 12%. i) For how much did he sell one
2.
Akinyi bought maize and beans from a wholesaler. She then mixed the maize and beans in the ratio 4: 3. She bought the maize at sh. 21 per kg and the beans at sh. 42 per kg. If she was to make a profit of 30%, what should be the selling price of 1 kg of the mixture?
3.
A retailer bought 40 kg of grade 1 rice at sh.65 per kilogram and 60 kg of grade II rice at sh 27.50 per kilogram. He mixed the two types of rice. (a) Find the buying price of one kilogram of the mixture. (b) He packed the mixture into 2 kg packets. (i) If he intends to make a 20% profit fin the selling price per packet. (ii) He sold 8 packets and then reduced the price by 10% in order to
4.
A trader sells a bag of beans for sh 2,100 and that of maize for sh 1,200. 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.
5.
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 and grade Z costs sh 256 per kg. (a) The dealer mixed grades X and Y in the ratio 5: 3 to make a brand of coffee which he sells at sh 180 per kg. Calculate the percentage profit he makes. (b) The dealer makes a new brand by mixing the three grades of coffee, in the ratios X:Y = 5: 3 and Y:Z
6.
Water and Milk are mixed such that the ratio of the volume of water to that of milk is 4 : 1. Taking the density of water as 1 g/#cm^3# and that of milk as 1.2 g/#cm^3#, find the mass, in grams of 2.5 litres of the mixture.
7.
A trader deals in two types of rice; type A and type B. Type A costs Ksh 400 per bag and type B costs Ksh 350 per bag. (a) The trader mixes 30 bags of type A with 50 bags of type B. If he sells the mixture at a profit of 20 %, calculate the selling price of one bag of the mixture. (b) The trader now mixes type A with type B in the ratio x : y respectively. If the cost of the mixture is Ksh 383.5
8.
A tea dealer mixes two brands of tea, x and y, to obtain 35 kg of the mixture worth Ksh 62 per kg. If brand x is valued at Ksh 68 per kg and brand y at Ksh 53 per kg, calculate the ratio, in its simplest form, in which the brands x and y are mixed.
9.
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.
10.
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
11.
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 : beans per kilogram in the mixture.
12.
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.
13.
Two types of flour, X and Y, cost ksh 60 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.
14.
A company is to construct a parking bay whose area is 135 #m^2#. It is to be covered with a concrete slab of uniform thickness of 0.15 m. To make the slab, cement, ballast and sand are to be mixed so that their masses are in the ratio 1:4:4. The mass of 1 #m^2# of dry slab is 2,500 kg. (a) Calculate (i) the volume of the slab (ii) the mass of the dry slab. (iii) the mass of cement to the used.
15.
Given that the ratio x:y = 2:3, find the ratio (5x2y) : (x+y)
16.
A hot water tap can fill a bath in 5 minutes while a cold water tap can fill the same bath in 3 minutes. The drain pipe can empty the full bath in #3 3/4# minutes. The two taps and the drain pipe are fully open for #1 1/2#minutes after which the drain pipe is closed. How much longer will it take to fill the bath?
17.
Mogaka and Onduso working together can do a piece of work in 6 days. Mogaka, working alone takes 5 days longer than Onduso. How many days does it take Onduso to do the work alone?
18.
A construction firm has two tractors #T_1# and #T_2#. Both tractors working together can complete piece of work in 6 days while #T_1# alone can complete the work in 15 days. After the two tractors had worked together for four days, tractor #T_1# broke down. Find the time taken by tractor #T_2# to complete the remaining work.
19.
Kipketer can cultivate a piece of land in 7 hours while Wanjiku can do the same work in 5 hours. Find the time they would take to cultivate the piece of land when working together.
20.
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.
21.
A farmer has two tractors A and B. The tractors, working together can plough a farm in #2 1/2# h. One day, the tractors started to plough the farm together. After 1 hour 10 min, tractor B broke down but A continued alone and completed the job after a further 4 h. Find: (a) The fraction of the job done by the tractors, working together for one hour.
22.
Pipe A can fill an empty water tank in 3 hours while, pipe B can fill the same tank in 6 hours. When the tank is full it can be emptied by pipe C in 8 hours. Pipes A and B are opened at the same time when the tank is empty. If one hour later, pipe C is opened find the total time taken to fill the tank.
23.
A tank has two inlet taps P and Q and an outlet tap R. When empty, the tank can be filled by tap P alone in #4 1/2# hours or by tap Q alone in 3 hours. When full, the tank can be emptied in 2 hours by tap R. (a) The tank is initially empty. Find how long it would take to fill up the tank: (i) If tap R is closed and taps P and Q are opened at the same time.
24.
An inlet tap can fill an empty tank in 6 hours. It takes 10 hours to fill the tank when the inlet tap and an outlet tap are both opened at the same time. Calculate the time the outlet tap takes to empty the full tank when the inlet tap is closed.
25.
Two taps A and B can each fill an empty tank in 3 hours and 2 hours respectively. A drainage tap R can empty the full tank in 6 hours. Taps A and R are opened for 5 hours then closed. (a) Determine the fraction of the tank that is still empty. (b) Find how long it would take to fill the remaining fraction of the tank if all the three taps are opened.
26.
Twenty five machines working at a rate of 9 hours per day can complete a job in 16 days. A contractor intends to complete the job in 10 days using similar machines working at rate of 12 hours per day. Find the number of machines the contractor requires to complete the job.
27.
Eleven people can complete #3/4#of a certain job in 24 hours. Determine the time in hours, correct to 2 decimal places, that 7 people working at the same rate take to complete the remaining job.
28.
Three works, working 8 hours per day can complete a task in 5 days. Each workers is paid Ksh. 40 per hour. Calculate the cost of hiring 5 workers if they work for 6 hours per day to complete the same task.
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