Refer to the data below and answer the questions that
follow
Ten electrical equipments (denoted by circles) are connected using wire connec ons as shown below. The figures within the circles denote the electric energy that the equipment consumes. The figure next to a par cular circle denotes its equipment number. For example: Equipment 1 consumes 50 units while equipment 5, consumes ‘A’ units. The figures next to a par cular wire connec on denote the electric energy the line carries. There was no loss of electric energy at any equipment i.e., the sum of the amount of electric energy leaving the equipment and that consumed by the equipment is equal to the amount of electric energy entering the equipment. At least one unit of electric energy must flow through all the lines. Also, the flow through each line has to be a posi ve integer.
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1. What will be the average amount of electric energy consumed by equipment 5 and equipment 6?
75
100
125
150
As, there was no loss of energy, 100 + 150 + 200 + 200 = 50 + 100 + 50 + 100 + A + B + 55 + 10 + 20 + 65 On simplifying, we get A + B = 200 ∴ The average amount of electric energy consumed by equipments A and B = 100. Hence, [2]
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2. How many values can 'x' take?
3
23
68
28
The minimum value of x = 1 As, there was no loss of energy,100 + 150 + 200 + 200 = 50 + 100 + 50 + 100 + A + B + 55 + 10 + 20 + 65 On simplifying, we get A + B = 200 Energy consumed by first 7 equipments = 50 + 100 + 50 + 100 + (A + B) + 55 = 50 + 100 + 50 + 100 + 200 + 55 = 555 Hence, energy outflow from equipment 5, 6, 7 = 650 – 555 = 95 As energy outflow from equipment A (i.e., the fifth equipment) was 25 units, 95 – 25 = 70 units flow out from the 6 and the 7 equipment. Minimum energy inflow in the 7 equipment = 100 + 1 = 101 units ⇒ Minimum outflow of energy from the 7 equipment = 101 55 = 46 Thus, maximum outflow of energy from the 6 equipment = 70 – 46 = 24 units Of these 24 units, at least 1 unit of energy flows towards the 8 equipment. Therefore, the maximum value of x = 24 – 1 = 23 units Thus, 'x' can take values from 1 to 23. Hence, [2].
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3. What can be the maximum amount of electric energy flowing through the line connecting equipment 8 and equipment 10?
13 units
64 units
38 units
39 units
As, there was no loss of energy,100 + 150 + 200 + 200 = 50 + 100 + 50 + 100 + A + B + 55 + 10 + 20 + 65 On simplifying, we get A + B = 200 Energy consumed by first 7 equipments = 50 + 100 + 50 + 100 + (A + B) + 55 = 50 + 100 + 50 + 100 + 200 + 55 = 555 Hence, energy outflow from equipment 5, 6, 7 = 650 – 555 = 95 As energy outflow from equipment A (i.e., the fifth equipment) was 25 units, 95 – 25 = 70 units flow out from the 6 and the 7 equipment. Minimum energy inflow in the 7 equipment = 100 + 1 = 101 units ⇒ Minimum outflow of energy from the 7 equipment = 101– 55 = 46 Thus, maximum outflow of energy from the 6 equipment = 70 – 46 = 24 units The minimum value of x = 1 Therefore, the maximum inflow in equipment 8 = 25 + (24 – 1) = 48 units 10 units energy was consumed by equipment 8. Therefore, a maximum of 48 – 10 = 38 units of energy could flow through the line connecting the equipment 8 and equipment 10. Hence, [3].
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4. Which of the following cannot be the amount of electric energy flowing between equipment 6 and equipment 8?
1
13
14
24
The minimum value of x = 1 As, there was no loss of energy,100 + 150 + 200 + 200 = 50 + 100 + 50 + 100 + A + B + 55 + 10 + 20 + 65 On simplifying, we get A + B = 200 Energy consumed by first 7 equipments = 50 + 100 + 50 + 100 + (A + B) + 55 = 50 + 100 + 50 + 100 + 200 + 55 = 555 Hence, energy outflow from equipment 5, 6, 7 = 650 – 555 = 95 As energy outflow from equipment A (i.e., the fifth equipment) was 25 units, 95 – 25 = 70 units flow out from the 6 and the 7 equipment. Minimum energy inflow in the 7 equipment = 100 + 1 = 101 units ⇒ Minimum outflow of energy from the 7 equipment = 101 55 = 46 Thus, maximum outflow of energy from the 6 equipment = 70 – 46 = 24 units Of these 24 units, at least 1 unit of energy flows towards the 9 equipment. Therefore the maximum amount of energy that can flow between equipment 6 and equipment 8 must be 23. Hence, [4].
