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Q:

In a public bathroom there are n taps 1,2,3...n. Tap1 and Tap2 take equal time to fill the tank while Tap3 takes half the time taken by Tap2 and Tap4 takes half the time taken by Tap3. Similarly each next number of tap takes half the time taken by previous number of Tap i.e, K-th  Tap takes half the time taken by (K-1)th Tap.

If the 10th tap takes 2 hours to fill the tank alone then what is the ratio of  efficiency of 8th tap and 12th tap, respectively?

A) 4:1 B) 5:3
C) 16:1 D) 1:16

Answer:   D) 1:16

Explanation:

Time taken by 8th tap = \inline 2\times 2\times 2 = 8 hours

and time taken by 12th tap = \inline 2\times \frac{1}{2}\times \frac{1}{2} = \inline \frac{1}{2} hour

Ratio of time taken by 8th 8th tap and 12th tap = \inline 8:\frac{1}{2} =16:1

Therefore, Ratio of efficiencies of 8th tap and 12th tap =1:16

Q:

A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in ?

A) 3 hrs B) 6 hrs
C) 7 hrs D) 5 hrs
 
Answer & Explanation Answer: B) 6 hrs

Explanation:

Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
6/x = 1/2 => x = 12
So, B takes 6 hours to finish the work.

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Q:

A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in --- days  ?

A) 51/24 B) 87/5
C) 57/12 D) 60/11
 
Answer & Explanation Answer: D) 60/11

Explanation:

A can complete the work in 12 days working 8 hours a day

=> Number of hours A can complete the work = 12×8 = 96 hours

=> Work done by A in 1 hour = 1/96

B can complete the work in 8 days working 10 hours a day

=> Number of hours B can complete the work = 8×10 = 80 hours

=> Work done by B in 1 hour = 1/80

Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480

=> A and B can complete the work in 480/11 hours

A and B works 8 hours a day

 Hence total days to complete the work with A and B working together

= (480/11)/ (8) = 60/11 days

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Q:

K can build a wall in 30 days. L can demolish that wall in 60 days. If K and L work on alternate days, when will the wall be completed ?

A) 120 days B) 119 days
C) 118 days D) 117 days
 
Answer & Explanation Answer: D) 117 days

Explanation:

K's work in a day(1st day) = 1/30
L's work in a day(2nd day)= -1/60(demolishing)
hence in 2 days, combined work= 1/30 - 1/60
=1/60
since both works alternatively, K will work in odd days and L will work in even days.
1/60 unit work is done in 2 days
58/60 unit work will be done in 2 x 58 days = 116 days
Remaining work = 1-58/60
= 2/60
= 1/30
Next day, it will be K's turn and K will finish the remaining 1/30 work.
hence total days = 116 + 1 = 117.

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Q:

A contractor undertook to complete a piece of work in 120 Days and employed 140 men upon it. At the end of 66 days only half of the work was done,so he put on 25 extra men. By how much time did he exceed the specific time ?

A) 2 days B) 3 days
C) 4 days D) 5 days
 
Answer & Explanation Answer: A) 2 days

Explanation:

work done=total number of person x number of days;
half of work done = 140 x 66;
For half of remaining work 25 extra men are added.
Therefore, total men for half work remaining = 140 + 25 = 165;
Let 2nd half work will be completed in K days;
140 x 66 = 165 x K
K = 122;
Hence, extra days => 122-120 = 2days.

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Q:

A,B,C together can do a piece of work in 10 days.All the three started workingat it together and after 4 days,A left.Then,B and C together completed the work in 10 more days.In how many days can complete a work alone ?

A) 25 B) 24
C) 23 D) 21
 
Answer & Explanation Answer: A) 25

Explanation:

(A+B+C) do 1 work in 10 days.
So (A+B+C)'s 1 day work=1/10 and as they work together for 4 days so workdone by them in 4 days=4/10=2/5
Remaining work=1-2/5=3/5
(B+C) take 10 more days to complete 3/5 work.
So( B+C)'s 1 day work=3/50
Now A'S 1 day work=(A+B+C)'s 1 day work-(B+C)'s 1 day work=1/10-3/50=1/25
A does 1/25 work in in 1 day
Therefore 1 work in 25 days.

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