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Difficulty:
15%
(low)
Question Stats:
81% (01:46) correct
19%
(02:13)
wrong
based on 520
sessions
History
Date
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Working at their respective constant rates, printing machine X, Y, and Z can finish a certain work in 9, 12, and 18 hours. If three machines work together to finish the work, what fraction of the work will be finished by the machine Z?
(A) 4/9
(B) 1/3
(C) 1/4
(D) 2/9
(E) 1/9
(A) 4/9
(B) 1/3
(C) 1/4
(D) 2/9
(E) 1/9
17 Feb 2011, 19:47
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banksy
Since time taken by X, Y and Z is in the ratio 9:12:18 i.e. 3:4:6,
their speeds are in the ratio \(\frac{1}{3}:\frac{1}{4}:\frac{1}{6} = 4:3:2\)
So Z will do \(\frac{2}{(4+3+2)} = 2/9\) of the work
18 Feb 2011, 01:48
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X; 9 hour-> 1 work
=> 1 hour -> 1/9 work
Y; 12 hour-> 1 work
=> 1 hour-> 1/12 work
Z; 18 hour-> 1 work
=> 1 hour-> 1/18 work
Total work done by all machines in 1 hour;
1/9+1/12+1/18 = (4+3+2)/36=9/36=1/4 work
Jointly;
1/4 work-> 1 hour
1 work-> 1/(1/4) = 4 hours(Jointly X,Y,Z all spent for 4 hours towards completing the job)
We know from before;
Z; 18 hour-> 1 work
=> 1 hour-> 1/18 work
If Z can perform 1/18 work in 1 hour;
In 4 hours, he would have performed
(1/18)*4 work
2/9 work
Ans: 2/9
=> 1 hour -> 1/9 work
Y; 12 hour-> 1 work
=> 1 hour-> 1/12 work
Z; 18 hour-> 1 work
=> 1 hour-> 1/18 work
Total work done by all machines in 1 hour;
1/9+1/12+1/18 = (4+3+2)/36=9/36=1/4 work
Jointly;
1/4 work-> 1 hour
1 work-> 1/(1/4) = 4 hours(Jointly X,Y,Z all spent for 4 hours towards completing the job)
We know from before;
Z; 18 hour-> 1 work
=> 1 hour-> 1/18 work
If Z can perform 1/18 work in 1 hour;
In 4 hours, he would have performed
(1/18)*4 work
2/9 work
Ans: 2/9
