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17 Oct 2025, 02:19
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A
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Difficulty:
25%
(medium)
Question Stats:
80% (01:12) correct
20%
(01:09)
wrong
based on 79
sessions
History
Date
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Machine A, machine B, and machine C, working together at their respective constant rates, can complete a certain job in 24 hours. How many hours would it take machine A, working alone at its constant rate, to complete the same job?
(1) Machines B and C, working together at their respective constant rates, can complete the job in 36 hours.
(2) Machines A and C, working together at their respective constant rates, can complete the job in 48 hours.
(1) Machines B and C, working together at their respective constant rates, can complete the job in 36 hours.
(2) Machines A and C, working together at their respective constant rates, can complete the job in 48 hours.
17 Oct 2025, 03:00
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Using Statement 1 alone:
Let total work be 72 units
And a, b, c be respective efficiencies of them
We have 24(a+b+c) = 72
a+b+c = 3
And 36(b+c) = 72
b+c = 2
Therefore, a = 1
Hence, A will complete the Total work in 72 hours with the efficiency of 1u/h
Sufficient
Using Statement 2 alone:
Let total work be 48 units
We have 24(a+b+c) = 48
a+b+c = 2
And 48(a+c) = 48
a+c = 1
Here we don't have the efficiency of A alone
Therefore, Not Sufficient
Hence, A
Let total work be 72 units
And a, b, c be respective efficiencies of them
We have 24(a+b+c) = 72
a+b+c = 3
And 36(b+c) = 72
b+c = 2
Therefore, a = 1
Hence, A will complete the Total work in 72 hours with the efficiency of 1u/h
Sufficient
Using Statement 2 alone:
Let total work be 48 units
We have 24(a+b+c) = 48
a+b+c = 2
And 48(a+c) = 48
a+c = 1
Here we don't have the efficiency of A alone
Therefore, Not Sufficient
Hence, A
17 Oct 2025, 21:21
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Machine A, machine B, and machine C, working together at their respective constant rates, can complete a certain job in 24 hours. How many hours would it take machine A, working alone at its constant rate, to complete the same job?
A+B+C=1/24 ......(1)
A=?
(1) Machines B and C, working together at their respective constant rates, can complete the job in 36 hours.
B+C=1/36......(With 1)
A+(1/36)=1/24
A=(1/24)-(1/36)=(3-2/72)=1/72
A alone takes 72 hours to complete the job.
Sufficient
(2) Machines A and C, working together at their respective constant rates, can complete the job in 48 hours.
A+C=1/48
A+B+((1/48)-A) =1/24
B=1/24-1/48 =1/48
we can find B’s speed from it, we still don’t know how much work A and C each do individually. So we can’t find A’s time alone.
Insufficient
A
A+B+C=1/24 ......(1)
A=?
(1) Machines B and C, working together at their respective constant rates, can complete the job in 36 hours.
B+C=1/36......(With 1)
A+(1/36)=1/24
A=(1/24)-(1/36)=(3-2/72)=1/72
A alone takes 72 hours to complete the job.
Sufficient
(2) Machines A and C, working together at their respective constant rates, can complete the job in 48 hours.
A+C=1/48
A+B+((1/48)-A) =1/24
B=1/24-1/48 =1/48
we can find B’s speed from it, we still don’t know how much work A and C each do individually. So we can’t find A’s time alone.
Insufficient
A
