BANK & INSURANCE (TIME AND WORK & PIPE AND CISTERN) PART 1

Total Questions: 60

21. A bathtub can be filled by the cold water pipe in 10 min and by hot water pipe in 15 min (independently each). A person leaves the bathroom after turning on both the pipes simultaneously and returns at the moment when the bath should have been full. But finds, that the waste pipe has been open, he now closes it. In 4 min more, bathtub is full. In what time will the waste pipe empty it?

Correct Answer: (a) 9 min  
Solution:

Let us assume some time l.c.m (10, 15) min = 30 min
Now in 30 min time cold water pipe will fill the bathtub 30/10 = 3 times whereas hot water pipe will fill it 30/15 = 2 times.
So in 30 min time bathtub will be filled 3+2 = 5 times.
So emptied bathtub will be fully filled in 30/5 = 6 min time if waste pipe is closed.

Initially waste pipe is opened and after 6 mins the waste pipe is closed, it takes 4 more minutes to fill the bathtub fully.
So waste pipe has emptied 4/6 = 2/3 part of bathtub in 6 mins
Rest 1/3 part of tank can be emptied by the waste pipe in 6/2 = 3 mins.
So waste pipe would empty the tank in 6+3 = 9 mins

22. A tank has 4 inlet pipes. Through the first 3 inlet pipes, the tank can be filled in 12 min; through the second, third, fourth inlet pipes, it can be filled in 15 minutes; and through the first and the fourth inlet pipes in 20 minutes. How much time will it take all the second and third inlet pipes alone to fill up the tank?

Correct Answer: (d) 20 minutes  
Solution:Let X, Y, Z, W be the inlet pipes
1/X + 1/Y + 1/Z = 1/12
1/Y + 1/Z + 1/W = 1/15
1/X + 1/W = 1/20
Adding the 3 equations,
2 (1/X + 1/Y + 1/Z + 1/W) = 1/12 + 1/15 + 1/20 = 12/60 = 1/5
1/X + 1/Y + 1/Z + 1/W = 1/10
1/Y + 1/Z = 1/10 - (1/X + 1/W) = 1/10 - 1/20 = 1/20
So second and third pipes can fill the tank in 20 minutes

23. A and B together can do a piece of work in 12 days, B and C together can do it in 18 days. If A and B started the work and A left after 4 days. Then C joined B and B left on the 6th day of the work. C finished it working for 17 days, then in how many days can A alone finish the work?

Correct Answer: (d) 108/7 days  
Solution:

C worked alone for 15 days (because for the first 2 days he worked with B), A and B worked together for 4 days and B and C together worked for 2 days.
So total work done by A and B in 4 days = 4 × (1/12) = 1/3
So total work done by B and C in 2 days = 2 × (1/18) = 1/9
So the total work done by C in 15 days = 1 - 1/3 - 1/9 = 5/9
So work done by C in 1 day = (5/9)/15 = 1/27.
So C can do the whole work in 27 days.
It is given that B and C together can do the work in 18 days
Hence work done by B in one day = 1/18 - 1/27 = 1/54
Means B can complete in 54 days.
Similarly A and B can finish the work in 12 days.
So work done by A in one day = 1/12 - 1/54 = 7/108
Hence A can complete the work in 108/7 days

24. A and B started working on a project and finished it in 5 days. If A had worked twice as efficiently and B worked at only half of his efficiency then the same job could have been completed in 4 days. If the total pay for the work is Rs 10000 then what is the share of A?

Correct Answer: (a) Rs 5000  
Solution:Suppose A can finish the work in a days and B can finish the work in b days.
Work done by A is 1/a unit and work done by B is 1/b unit.
According to the 1st condition they finish the work in 5 days. It means they complete 1/5 of work in one day.
Therefore, 1/a + 1/b = 1/5
Now according to 2nd condition A worked twice as efficiently so he will be able to finish the work in half the time as compared to what he took when he worked at normal speed. So at twice efficiency A will take a/2 days to finish the work and similarly B will take 2b days to finish the work.
So, 2/a + 1/(2b) = 1/4
Now solving Eq(1) and Eq(2) we will get, a = 10 and b = 10
They do same amount of work every day, hence share of A = Rs (10000)/2 = Rs 5000

25. Sandeep works for 12 hours and prints 18 pages per hour, Navdeep works for 8 hours and prints 20 pages per hour and then stops working. After 2 hours Navdeep again starts working and works for 2 more hours with efficiency 18 pages per hour and Pradeep works for 15 hours and prints 16 pages per hour. If total earning of all of them together is Rs.4890, then find the share of Sandeep.

Correct Answer: (d) Rs.1620  
Solution:

Ratio of share of their work = (12 × 18) : (8 × 20 + 2 × 18) : (15 × 16) = 216 : 196 : 240 = 54 : 49 : 60
Ratio of share of earning = Ratio of amount of work done
Share of Sandeep = 4890 × (54/163) = Rs.1620

26. If twenty persons can complete 4/5th of the work in twelve days, then find how many more persons will be required to complete the remaining work in one and a half days.

Correct Answer: (c) 20
Solution:

Let the working capacity of one man be M.
Number of persons × work doing capacity of one person × number of days = amount of work done
=> 20 × M × 12 = 4/5
=> M = (4/5) / (20 × 12)
=> M = 1/300
Let the number of persons added = x
Work remaining = 1 - 4/5 = 1/5
=> (20 + x) × M × 1.5 = 1/5
=> (20 + x) × (1/300) × 1.5 = 1/5
=> (20 + x) × (1/300) × 1.5 = 1/5
=> X = 20 more persons.

27. A can build a wall in 40 days and B can break the same wall in 60 days. A has worked for 5 days and after that B also joined A. A and B together worked for 30 days after that B left the work and A kept on working. In how many total days the wall will be constructed?

Correct Answer: (a) 60 days  
Solution:Total wall build by A in 5 days = 5 × (1/40) = 1/8
Now work done by A and B together in one day by working alone = (1/40) - (1/60) = 1/120
Total work done in 30 days = 30/120 = 1/4
Total work completed in 35 days = (1/8) + (1/4) = 3/8
Remaining work = 1 - (3/8) = 5/8
Let's suppose A take 'N' days to build the remaining wall while working alone.
Therefore; (1/40) × N = 5/8
=> N = (5×40)/8
=> N = 25 days
Therefore total number of days to build the wall = (5 + 30 + 25) = 60 days

28. A builder undertakes a contract of a building, which is to be completed in 1 month (April). He employed 10 workers of equal efficiency but at the end of 2/3rd of month, 58 1/3 % of work was remaining, so he employed some more workers to finish the work on time. Wage of 1 worker is Rs.625/day, then find how much total wage is given to the extra workers which are employed to finish the work in time.

Correct Answer: (b) Rs.112500  
Solution:

Let 1 worker completes the work in 'n' days
Then,
Work done by 10 workers in 1 day = 10/n
April = 30 days
2/3rd month = 20 days
=> 20 × 10/n = (100 - 175/3)/100
=> n = 20000 × 3/125
=> n = 480
So, 1 worker alone can complete the work in 480 days.
If 'y' more workers are employed for 10 days as the work is to be completed in 30 days, then,
=> (10 + y) × 10/480 = 175/300
=> y = 18
So, 18 more workers are employed, and wage of 1 worker is Rs.625.
So, wage given to extra workers employed = 18 × 625 × 10 = Rs.112500

29. A purifier had a total of 15 valves among which few were connected to fill the purifier while the rest of the valves were used to drain the purified water. Each of the valves used for the purpose of filling could fill the purifier in 15 hours while each of the draining valves would take 30 hours to drain the purifier. If all the pipes are kept open and if it took 2 hours to completely fill the purifier then what % of the total pipes were reserved for draining purpose?

Correct Answer: (a) 33.33%  
Solution:

Let the number of valves allotted to fill the tank be 'y'.
The number of valves allotted for draining purpose will be (15 - y)
A value used for filling fills the purifier in 15 hours.
So, in 1 hour it can fill 1/15th part of the purifier.
Similarly, a value used for draining drains the purifier in 30 hours. So, in 1 hour it can drain 1/30th part of the purifier.

Given, it took 2 hours to fill with all valves open. So, the equation becomes
(2xy)/15 - (2x(15-y))/30 = 1
On solving, we get y = 10
Therefore number of valves allotted to fill the purifier = 10
The number of valves allotted to drain the purifier will be 5
Percentage of valves allotted for draining purpose = 5/15 × 100 = 33.33%

30. Two men undertake to do a piece of work for Rs.1400. The first man alone can do this work in 7 days while the second man alone can do this work in 8 days. If they working together complete this work in 3 days with the help of a boy, how should the money be divided?

Correct Answer: (b) Rs.600, Rs.525, Rs.275
Solution:

Work done by first man in one day = 1/7th of total work
Work done by second man in one day = 1/8th of total work
Let the work done by a boy in one day be 1/a of total work
Therefore, work done by all three of them in one day
= 1/7 + 1/8 + 1/a = 1/3
1/a = 1/3 - 1/7 - 1/8 = 11/168, or a = 168/11
Hence, boy would take (168/11) days to finish the work
Work done by first man in 3 days = 3/7
Work done by second man in 3 days = 3/8
Work done by boy in 3 days = 11/56
Ratio of their wages = (3/7) : (3/8) : (11/56)
= 24 : 21 : 11
First man's share = 1400 × 24/56 = Rs. 600
Second man's share = 1400 × 21/56 = Rs. 525
Boy's share = Rs 275