 # Time & Work (8)

1. Ram starts working on a job and works on it for 12 days and completes 40% of the work. To help him complete the work, he employs Ravi and together they work for another 12 days and the work gets completed. How much more efficient is Ram than Ravi?
1. 50%
2. 200%
3. 125%
4. 100%

Explanation :-

Lets suppose Ram completes the work in x days & Ravi completes the work in y days
Ram’s one day work = 1/x  &   Ravi’s one day work = 1/y
As Ram completes 40% of work , therefore , Ram’s one day work
Ram’s one day work = (work to complete ) / (time)
1/x =  (40/100) / (12)
x = 30
Remaing work (60%) is done by both of them in 12 adys
Therefore , (1/30)
[(1/30) *12] + [(1/y)*12] = 60/100
12(1/y) = (3/5) – (2/5)
(1/y) = (1/5) * (1/12)
y = 60
Ram completes the work in 30 days
Ravi completes the work in 60 days
So , Ram is 100% more efficient than Ravi

2. Two taps can fill a tank in 12 min and 18 min respectively. Both the taps are kept open for 2 min and then the tap that fills the tank in 12 min is turned off. In how many more minutes will the tank be filled?
1.  9
2. 12
3. 13
4. 10

Explanation :-

Part of tank filled by tap1 in 1 minute = 1/12
Part of tank filled by tap2 in 1 minute = 1/18
In 2 minutes, Part of tank filled by both taps = 2[(1/12)+(1/18)] =  (5/18) of the tank.
Remaing tank to be filled = 1 – (5/18) = 13/18
Time taken by tap2 to fill Remaing tank = (13/18)/(1/18) = 13 minutes

3. Pankaj can produce one unit in 15 days, while Bharti can do the same in 12 days. After producing one unit, working together, they received Rs. 90, which they distributed amongst themselves in proportional to their efficiency. If they work for 20 days, and sell the produce, then Bharti should receive
1. Rs. 120
2. Rs. 140
3. Rs. 150
4. Rs. 160

Explanation :-

In 1 day , Pankaj can produce (1/15) unit
In 1 day , Bharti can produce (1/12) unit
In 1 day , Together they can produce = [ (1/15) + (1/12) ] = 3/20
In 20 days, together they can produce = (3/20) * 20 = 3 units
Total money received = 3*90 = Rs.270
Ratio of Pankaj & Bharti ,s work = (1/15) : (1/12) = 12 : 15 = 4 : 5
Bharti’s share = (270/9)*5 = Rs 150

4. Pavan builds an overhead tank in his house, which has three taps attached to it. While the first tap can fill the tank in 12 hours, the second one takes one and a half times than the first one to fill it completely. A third tap is attached to the tank which empties it in 36 hours. Now one day, in order to fill the tank, Pavan opens the first tap and after two hours opens the second tap as well. However, at the end of the sixth hour, he realizes that the third tap has been kept open right from the beginning and promptly closes it. What will be the total time required to fill the tank?
1. 8 hours 48 minutes
2. 9 hours 12 minutes
3. 9 hours 36 minutes
4. 8 hours 30 minutes

Explanation :-

After 6 hours, part of tank filled by the three pipes.= (6/12) + (4/18) + (6/36) = 5/9
Remaing Part = 1- (5/9) = 4/9
The part pf tank is to be filled by A and B together.
A and B together can fill in one hour = (1/12) + (1/10) = 5/36
Remaing part can be filled in = (4/9)/(5/36) = 16/5 hours =  3 hours 12 minutes
Total time = 6 hours + 3 hours + 12 minutes = 9 hours 12 minutes

5. Yesterday Mansi typed an essay of 5000 words at the speed of 60 words per minute. Today she typed the same essay faster and her speed was 15% more than yesterday. What is the approximate difference in the time she took to type yesterday and the time she took to type today?
1. 20 minutes
2. 30 minutes
3. 10 minutes
4. 40 minutes
5. 1 hour