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20 Mar 2026, 22:01
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
79% (02:47) correct
21%
(02:58)
wrong
based on 84
sessions
History
Date
Time
Result
Not Attempted Yet
A toy factory has four assembly machines, A, B, C, and D, that operate at constant rates. To assemble a given number of toy cars, machine C takes three times as long as machine A, and machine B takes four times as long as machine C and twice as long as machine D. How long would it take machine A, working alone, to assemble the same number of toy cars that machines B, C, and D, working together, can assemble in 1 hour?
A. 30 minutes
B. 35 minutes
C. 40 minutes
D. 45 minutes
E. 50 minutes
A. 30 minutes
B. 35 minutes
C. 40 minutes
D. 45 minutes
E. 50 minutes
24 Mar 2026, 00:44
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C = 3A , B=4C and B=2D
Converting this into ratios A: B : C : D = 1 : 12 : 3 : 6. These are the time ratios.
Let’s shift to efficiency ratios, A: B : C : D =
(1/1) : (1/12) : (1/3) : (1/6)
Multiply by 12 throughout, we get
12: 1: 4 : 2
Combined efficiency of B, C and D is 7. So it has taken 1 hour to complete .
Total work = 7 * 60 mins . The same can be completed by A alone in ?
= (7*60)/12
= 35 mins
Option B
Converting this into ratios A: B : C : D = 1 : 12 : 3 : 6. These are the time ratios.
Let’s shift to efficiency ratios, A: B : C : D =
(1/1) : (1/12) : (1/3) : (1/6)
Multiply by 12 throughout, we get
12: 1: 4 : 2
Combined efficiency of B, C and D is 7. So it has taken 1 hour to complete .
Total work = 7 * 60 mins . The same can be completed by A alone in ?
= (7*60)/12
= 35 mins
Option B
12 Apr 2026, 10:11
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Deconstructing the Question
Let machine A take \(T_A\) hours to complete the job alone.
We are told that machine C takes \(3\) times as long as A, machine B takes \(4\) times as long as C, and machine B takes \(2\) times as long as D.
Work with times first, then convert to rates.
Step-by-step
Let the whole job be \(1\).
Then
\(T_C = 3T_A\)
Since B takes 4 times as long as C,
\(T_B = 4(3T_A) = 12T_A\)
Since B takes twice as long as D,
\(T_B = 2T_D\)
so
\(T_D = \frac{T_B}{2} = \frac{12T_A}{2} = 6T_A\)
Now convert to rates.
Rate of A:
\(\frac{1}{T_A}\)
Rate of B:
\(\frac{1}{12T_A}\)
Rate of C:
\(\frac{1}{3T_A}\)
Rate of D:
\(\frac{1}{6T_A}\)
Combined rate of B, C, and D:
\(\frac{1}{12T_A} + \frac{1}{3T_A} + \frac{1}{6T_A}\)
Rewrite with denominator \(12T_A\):
\(\frac{1}{12T_A} + \frac{4}{12T_A} + \frac{2}{12T_A} = \frac{7}{12T_A}\)
So in 1 hour, B, C, and D complete
\(\frac{7}{12T_A}\)
of the job.
How long would A take to complete that same amount of work?
\(\frac{\frac{7}{12T_A}}{\frac{1}{T_A}} = \frac{7}{12}\)
hour.
Convert to minutes:
\(\frac{7}{12}\cdot 60 = 35\)
Answer B
Let machine A take \(T_A\) hours to complete the job alone.
We are told that machine C takes \(3\) times as long as A, machine B takes \(4\) times as long as C, and machine B takes \(2\) times as long as D.
Work with times first, then convert to rates.
Step-by-step
Let the whole job be \(1\).
Then
\(T_C = 3T_A\)
Since B takes 4 times as long as C,
\(T_B = 4(3T_A) = 12T_A\)
Since B takes twice as long as D,
\(T_B = 2T_D\)
so
\(T_D = \frac{T_B}{2} = \frac{12T_A}{2} = 6T_A\)
Now convert to rates.
Rate of A:
\(\frac{1}{T_A}\)
Rate of B:
\(\frac{1}{12T_A}\)
Rate of C:
\(\frac{1}{3T_A}\)
Rate of D:
\(\frac{1}{6T_A}\)
Combined rate of B, C, and D:
\(\frac{1}{12T_A} + \frac{1}{3T_A} + \frac{1}{6T_A}\)
Rewrite with denominator \(12T_A\):
\(\frac{1}{12T_A} + \frac{4}{12T_A} + \frac{2}{12T_A} = \frac{7}{12T_A}\)
So in 1 hour, B, C, and D complete
\(\frac{7}{12T_A}\)
of the job.
How long would A take to complete that same amount of work?
\(\frac{\frac{7}{12T_A}}{\frac{1}{T_A}} = \frac{7}{12}\)
hour.
Convert to minutes:
\(\frac{7}{12}\cdot 60 = 35\)
Answer B
