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Q1. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long should it take both A and B, working together but independently to do the same job.
a) 40/9
b) 9/40
c) 20/9
d) None of these
A. (a)
As discussed in our tutorial
Amount of work done by A in 1 day : 1/8
Amount of work done by B in 1 day : 1/10
Amount of work done by (A+B) :
Both A and B will finish the work in : 40/9 days.
Q2. Worker A takes 10 hours to do a job. Worker B takes 15 hours to do the same job. How long should it take both A and B, working together but independently to do the same job.
a) 16
b) 10
c) 6
d) 8
A. (c)
As discussed in our tutorial
Amount of work done by A in 1 day : 1/10
Amount of work done by B in 1 day : 1/15
Amount of work done by (A+B) :
Both A and B will finish the work in : 6 days.
Q3. A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how days can B alone complete that work ?
a) 9
b) 4
c) 8
d) 6
A. (d)
As discussed in our tutorial
Amount of work done by A+B in 1 day : 1/4
Amount of work done by A in 1 day : 1/12
Amount of work done by (B) :
B will finish the work in : 6 days.
Q4. A and B can do a piece of work in 18 days, B and C can do it in 24 days, A and C can do it in 36 days. In how many days will A finish it, working separately ?
a) 36
b) 48
c) 18
d) 16
A. (b)
Amount of work done by A+B in 1 day : 1/18
Amount of work done by B+C in 1 day : 1/24
Amount of work done by A+C in 1 day : 1/36
On adding above three equations :
2(A + B + C) 1 day work =
(A + B + C) 1 day work :
Hence, it is quite evident that A B & C together can finish the work in 16 days.
Now, A’s 1 day work : (A + B + C) 1 day work – (B + C) 1 day work
So, A alone can finish the work in 48 days.
Q5. To complete a piece of work A and B take 8 days, B and C 12 days, A, B and C take 6 days. A and C will take :
a) 9
b) 4
c) 8
d) 6
A. (c)
Amount of work done by A+B in 1 day : 1/8
Amount of work done by B+C in 1 day : 1/12
Amount of work done by A+B+C in 1 day : 1/6
Work done by A alone :
(A+B+C)’s 1 day work – (B+C)’s 1 day work = A’s 1 day work
Work done by C alone :
(A+B+C)’s 1 day work – (A+B)’s 1 day work = C’s 1 day work
Now, (A+C)’s 1 day work :
=> 8 days.