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Two machines A and B worked at variable rates. The average number of items produced per day by machine A could be expressed as Ra (x) = ax(x + 1) and the average number of items produced per day by machine B could be expressed as Rb (x) = bx(x-1), where x was the number of consecutive days worked and a, b were constants. If machine B produced 90 more items when it worked for 4 consecutive days than when it worked for to 3 consecutive days and machine A produced a total of 232 items when it worked in two intervals of 3 consecutive days and 4 consecutive days, how many items was produced by machines A and B working together for 10 consecutive days?
  • a)
    3855
  • b)
    4485
  • c)
    4900
  • d)
    5200
  • e)
    5675
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two machines A and B worked at variable rates. The average number of i...
Given:
  • Average number of items produced per day by machine A , Ra (x) = ax(x + 1)
    • x is the number of consecutive days worked and a is a constant
    • Machine A produced 232 items when it worked for two intervals of 3 consecutive days and 4 consecutive days
  • Average number of items produced per day by machine B, Rb (x) = bx(x-1)
    • x is the number of consecutive days worked and b is a constant
    • Machine B produced 90 more items when it worked for 4 consecutive days than when it worked for 3 consecutive days
To Find: Number of items produced by machine A and B working together for 10 consecutive days
Approach:
  1. We know that Number of items produced = Rate of producing items * Time taken
    • As we are given the time taken to be 10 days, we need to find the rate of producing items for both machines A and B, i.e. we need to find the values of Ra (x) and Rb (x)
  2. For finding the values of R (x) and R (x), we need to find the values of a and b, i.e. we need an equation each in a and b.
  3. As we are given the number of items produced by machine A in a certain time interval and the number of items produced by machine B in a certain time interval, we will use this information to find the values of a and b.
Working out:
  1. Rate of producing items of machine A
    • Number of items produced working for 3 consecutive days = ax(x+1)*x = 3a(3+1) * 3 = 36a
    • Number of items produced working for 4 consecutive days = ax(x+1)*x= 4a(4+1) * 4 = 80a
    •  So, total number of items produced = 36a +80a = 116a = 232
    • a = 2
  2. Rate of producing items of machine B
    • Number of items produced working for 4 consecutive days = bx(x-1)*x = 4a(4-1) * 4 = 48b
    • Number of items produced working for 3 consecutive days = bx(x-1)*x = 3a(3-1) * 3 = 18b
    • So, extra items produced = 48b – 18b = 30b = 90
    • b = 3
  3. Number of items produced by machine A working for 10 consecutive days = ax(x+1)*x = 2*10 *(10+1)*10 = 2200
  4. Number of items produced by machine B working for 10 consecutive days = bx(x-1)*x = 3*10*(10-1)*10 = 2700
  5. Total number of items produced by machine A and machine B working together for 10 consecutive days = 2200 + 2700 = 4900
Answer : C 
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Two machines A and B worked at variable rates. The average number of items produced per day by machine A could be expressed as Ra (x) = ax(x + 1) and the average number of items produced per day by machine B could be expressed as Rb (x) = bx(x-1), where x was the number of consecutive days worked and a, b were constants. If machine B produced 90 more items when it worked for 4 consecutive days than when it worked for to 3 consecutive days and machine A produced a total of 232 items when it worked in two intervals of 3 consecutive days and 4 consecutive days, how many items was produced by machines A and B working together for 10 consecutive days?a)3855b)4485c)4900d)5200e)5675Correct answer is option 'C'. Can you explain this answer?
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