 # Time & Work (7)

1. There is a group of persons each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?
1. 3 1⁄4 days
2. 4 1⁄3 days
3. 5 1⁄6 days
4. 6 1⁄5 days

Explanation :-

Work done in 1st day(by 1 person) = 1/16
Work done in 2nd day (by 2 persons) = (1/16) + (1/16) = 2/16
Work done in 3rd day (by 3 persons) = (1/16) + (1/16) + (1/16) = 3/16
The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16
The work done in 4 days = (1+2+3+4)/16 = 10/16
The work done in 5 days = (1+2+3+4+5)/16 = 15/16, (near to 1)
The work done in 6 days = (1+2+3+4+5+6)/16 > 1
Remaining work in 6th day = 1 – 15/16 = 1/16.
In 6th day, 6 people are working ,
Therefore ,
Work done by 6 persons= 6/16.
TimeTaken to complete the work on sixth day = (1/16) / (6/16) = 1/6 days.
Hence total time required = 5 + 1/6 = 5 16 days

2. Work done by A in one day is half of the work done by B in one day. Work done by B is half of the work done by C in one day. If C alone can complete the work in 7 days, in how many days will A, B and C together will complete the work?
1. 28
2. 14
3. 4
4. 21

Explanation :-

C completes the work in 7 days  &  C’s 1 day work = 1/7
Therefore ,
B can complete the work in 2*7 days = 14 days  &  C’s 1 day work = 1/14
A can complete the work in 2*14 days = 28 days  &  A’s 1 day work = 1/28/
Work done by A , B & C together in one day = (1/7) +(1/14) + (1/28) = (4 + 2 + 1)/28 = 7/28 = 1/4
Therefore, They all together can complete the work in 4 days

3. Two pipes P and Q can fill a cistern in 12 minutes and 16 minutes respectively.  Simultaneously both the pipes are opened together, then after how much time Q should be closed so that the tank is full in 9
min ?
1. 3.5 min.
2. 4 min.
3. 4.5 min.
4. 4.75 min.
5. 5.00 min

Explanation :-

Let Q be closed after x min.
Part of cistern filled by (P+Q) in x min + part filled by P in ( 9 – x )min = 1
=> x[(1/12) + (1/16)] + [ (9x)(1/12)] 1
7x+36-4x=48
x = 4.
That means ‘Q’ must be closed after 4 minutes.

4. A leak in the lower portion of a tank can empty the full tank in 9 hrs.  An inlet pipe fills water at the rate of 10 lit. a minute.  When the tank is full, the inlet is opened and due to leak, the tank is empty in 16 hrs.  How many litres does the cistern hold ?
1. 17,580
2. 17,960
3. 18,290
4. 12,342
5. 13,500

Explanation :-

Work done by the inlet in 1 hr = (1/9) − (1/16) = (7/144) = 19−116=7144
Work done by the inlet in 1 min. = (7/144) × (1/607/8640
Volume of (7/8640) part = 10 litres
Whole volume = 10 × (8640/7) 12,342 litres.

5. 8 children and 12 men complete a certain piece of work in 9 days. If each child takes twice the time taken by a man to finish the work, in how many days will 12 men finish the same work ?
1. 8
2. 15
3. 9
4. 12
5. 14