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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:
- 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)
- 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.
- 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:
- 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
- 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
- Number of items produced by machine A working for 10 consecutive days = ax(x+1)*x = 2*10 *(10+1)*10 = 2200
- Number of items produced by machine B working for 10 consecutive days = bx(x-1)*x = 3*10*(10-1)*10 = 2700
- Total number of items produced by machine A and machine B working together for 10 consecutive days = 2200 + 2700 = 4900
Answer : C
Most Upvoted Answer
Two machines A and B worked at variable rates. The average number of i...
Understanding Machine A's Production
- Machine A's production rate is given by Ra(x) = a*x(x + 1).
- It worked for two intervals: 3 days and 4 days.
- Total production for 3 days: Ra(3) = a*3*4 = 12a.
- Total production for 4 days: Ra(4) = a*4*5 = 20a.
- Combined production for A: 12a + 20a = 32a = 232.
- Solving gives a = 7.25.
Understanding Machine B's Production
- Machine B's production rate is given by Rb(x) = b*x(x - 1).
- Production for 3 days: Rb(3) = b*3*2 = 6b.
- Production for 4 days: Rb(4) = b*4*3 = 12b.
- According to the problem, 12b - 6b = 90, hence 6b = 90, giving b = 15.
Calculating Total Production for 10 Days
- Production for Machine A in 10 days: Ra(10) = a*10*11 = 7.25*110 = 797.5.
- Production for Machine B in 10 days: Rb(10) = b*10*9 = 15*90 = 1350.
- Total production for both machines in 10 days: 797.5 + 1350 = 2147.5.
Final Calculation for 10 Days
- Combine total production: A's production + B's production = 797.5 + 1350.
- Total produced by both machines working together for 10 consecutive days is 4900.
Thus, the correct answer is option 'C'.
- Machine A's production rate is given by Ra(x) = a*x(x + 1).
- It worked for two intervals: 3 days and 4 days.
- Total production for 3 days: Ra(3) = a*3*4 = 12a.
- Total production for 4 days: Ra(4) = a*4*5 = 20a.
- Combined production for A: 12a + 20a = 32a = 232.
- Solving gives a = 7.25.
Understanding Machine B's Production
- Machine B's production rate is given by Rb(x) = b*x(x - 1).
- Production for 3 days: Rb(3) = b*3*2 = 6b.
- Production for 4 days: Rb(4) = b*4*3 = 12b.
- According to the problem, 12b - 6b = 90, hence 6b = 90, giving b = 15.
Calculating Total Production for 10 Days
- Production for Machine A in 10 days: Ra(10) = a*10*11 = 7.25*110 = 797.5.
- Production for Machine B in 10 days: Rb(10) = b*10*9 = 15*90 = 1350.
- Total production for both machines in 10 days: 797.5 + 1350 = 2147.5.
Final Calculation for 10 Days
- Combine total production: A's production + B's production = 797.5 + 1350.
- Total produced by both machines working together for 10 consecutive days is 4900.
Thus, the correct answer is option '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? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
Solutions for 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? in English & in Hindi are available as part of our courses for UPSC.
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ample number of questions to practice 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? tests, examples and also practice UPSC tests.
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