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25 Mar 2025, 00:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
86% (01:42) correct
14%
(01:39)
wrong
based on 65
sessions
History
Date
Time
Result
Not Attempted Yet
Machines A, B, and C produced identical bottles at different constant rates. In the first 2 hours, A alone operated and filled a part of the entire production lot; then B alone operated for 3 hours and filled another part of the entire lot, and finally, C alone operated for 4 hours and filled the rest of the entire lot. Which of the three machines filled the greatest part of the entire lot?
(1) The ratio of the constant rates at which A and B produced is 3 : 2.
(2) The ratio of the constant rates at which B and C produced is 4 : 3.
(1) The ratio of the constant rates at which A and B produced is 3 : 2.
(2) The ratio of the constant rates at which B and C produced is 4 : 3.
25 Mar 2025, 00:45
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Let the production rates of machines A, B, and C be \(a, b,\) and \(c\) bottles per hour, respectively.
Total production in each phase:
- A operates for 2 hours → produces \(2a\) bottles.
- B operates for 3 hours → produces \(3b\) bottles.
- C operates for 4 hours → produces \(4c\) bottles.
Statement (1)
\(\frac{a}{b} = \frac{3}{2}\)
This implies \(a = \frac{3}{2}b\).
Substituting in the production formula:
\(2a = 2 \times \frac{3}{2}b = 3b\).
Thus, the production contributions become:
- A: \(3b\)
- B: \(3b\)
- C: \(4c\)
Not sufficient
Statement (2)
\(\frac{b}{c} = \frac{4}{3}\)
This implies \(b = \frac{4}{3}c\).
Substituting in the production formula:
\(3b = 3 \times \frac{4}{3}c = 4c\).
Thus, the production contributions become:
- A: \(2a\)
- B: \(4c\)
- C: \(4c\)
Not sufficient
Combining (1) and (2):
From (1): \(a = \frac{3}{2}b\)
From (2): \(b = \frac{4}{3}c\)
Substituting \(b\) in the equation for \(a\):
\(a = \frac{3}{2} \times \frac{4}{3}c = 2c\)
Thus, the contributions become:
- A: \(2a = 4c\)
- B: \(3b = 4c\)
- C: \(4c\)
Since all machines contribute equally (4c each), no single machine filled the greatest part.
Final Answer: (C) Together, both statements are sufficient.
Total production in each phase:
- A operates for 2 hours → produces \(2a\) bottles.
- B operates for 3 hours → produces \(3b\) bottles.
- C operates for 4 hours → produces \(4c\) bottles.
Statement (1)
\(\frac{a}{b} = \frac{3}{2}\)
This implies \(a = \frac{3}{2}b\).
Substituting in the production formula:
\(2a = 2 \times \frac{3}{2}b = 3b\).
Thus, the production contributions become:
- A: \(3b\)
- B: \(3b\)
- C: \(4c\)
Not sufficient
Statement (2)
\(\frac{b}{c} = \frac{4}{3}\)
This implies \(b = \frac{4}{3}c\).
Substituting in the production formula:
\(3b = 3 \times \frac{4}{3}c = 4c\).
Thus, the production contributions become:
- A: \(2a\)
- B: \(4c\)
- C: \(4c\)
Not sufficient
Combining (1) and (2):
From (1): \(a = \frac{3}{2}b\)
From (2): \(b = \frac{4}{3}c\)
Substituting \(b\) in the equation for \(a\):
\(a = \frac{3}{2} \times \frac{4}{3}c = 2c\)
Thus, the contributions become:
- A: \(2a = 4c\)
- B: \(3b = 4c\)
- C: \(4c\)
Since all machines contribute equally (4c each), no single machine filled the greatest part.
Final Answer: (C) Together, both statements are sufficient.
25 Mar 2025, 02:03
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Bunuel
\(\frac{2}{A} + \frac{3}{B} + \frac{4}{C} = 1\)
We need to know about the rates of A, B and C to answer this question
Question: Which machine gave the maximum output?
Statement 1: The ratio of the constant rates at which A and B produced is 3 : 2.
This statement is NOT sufficient because we don't know about C and the rates of A and B could be 3 and 2 hours while rates could be 6 and 4 hours etc.
NOT SUFFICIENT
Statement 2: The ratio of the constant rates at which B and C produced is 4 : 3.
If rates of B and C are 8 and 6 then it would give different output of A than when the rates of B and C are 20 and 15 hence
NOT SUFFICIENT
Combining the statements
A:B = 3:2 and B:C = 4:3
i.e. A:B:C = 6:4:3
let, A rate = 6, B = 4 and C = 3
Work of A = 6*2(for 2 hours) = 12
Work of A = 4*3(for 4 hours) = 12
Work of A = 3*4(for 4 hours) = 12
So their work are equal
SUFFICIENT
Answer: Option C
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