## Time and Work Practice Problems – Set 4

Time and Work Practice Problems – Set 4
Direction (1 – 3): Study the following information carefully and answer the following questions given below -
Amit can do a work in 30 days, while Sumit can do the same work in 45 days. They started the work together. After X days, Romit also joined them and thus all of them completed the whole work in 12 days. A total of Rs.750 is paid to all of them.
1. What is the Share of Romit?
a) Rs.250
b) Rs.300
c) Rs.350
d) Can’t be determined
e) None of these
Explanation:
Amit = 30 days; Sumit = 45 days
LCM = 90 units
Amith’s units = 90/30 = 3 units; Sumit’s units = 90/45 = 2 units
Total units of both = 5 units
Work Done = 5 * 12 = 60 units
Remaining = 90 – 60 = 30 units
Work done by Romit = 30 units
Work done by Amit = 12 * 3 = 36 units
Work done by Sumit = 12 * 2 = 24 units
Romit’s share = 750 * 30/90 = 250

2. What is the value of X?
a) 5
b) 6
c) 7
d) Can’t be determined
e) None of these
Explanation:
Efficiency of Romit is not given. So answer can’t be determined

3. If the value of X is 7, then Amit’s efficiency to Romit is how much percent?
a) 40%
b) 50%
c) 80%
d) 120%
e) None of these
Explanation:
Romit worked for 12 – 7 = 5 days
Romit’s units = 30/5 = 6
Amit’s units = 3
Efficiency % = 3/6 * 100 = 50%

Directions (4 – 5): Study the following information carefully and answer the questions given below
Working together Ram and Sham take 33.33% more number of days than Ravi, Ram and Sham together take. Ravi, Ram and Sham all worked together till the completion of the work and Ram received Rs.240 out of total wage of Rs. 720.
4. In how many days did Ravi, Ram and Sham together complete the whole work?
a) 2 days
b) 4 days
c) 5 days
d) 6 days
e) 7 days
Explanation:
Ravi, Ram and sham : Ram and Sham
Days 3 : 4
Units 4 : 3
Ravi’s unit = 4 – 3 = 1
Ravi’s share = 720 * 1/4 = 180
Ram’s share = 240
Sham’s share = 300
Work ratio = Ravi : Ram : Sham = 3 : 4 : 5 == 12
LCM = 60
Total days together = 60/12 = 5 days

5. If the whole work done by only Ravi and Sham together, then find the share of each?
a) Rs.270 and Rs.450
b) Rs.300 and Rs.420
c) Rs.350 and Rs.370
d) Rs.360 and Rs.360
e) None of these
Explanation:
Share of Ravi = 720 * 3/8 = 270
Share of Sham = 720 * 5/8 = 450

6. Mohan and Sohan working separately can dig a trench in 10 days and 12 days respectively. If they are working for 1 day alternately, Mohan beginning, in how many days will the trench be dug?
a) 11 3/2 days
b) 10 5/6 days
c) 9 5/7 days
d) Can’t be determined
e) None of these
Explanation:
Mohan’s 1 day work = 1/10; Sohan’s 1 day work = 1/12
For two days total work done = 1/10 + 1/12 = 11/60
For 10 days total work done = 5 * 11/60 = 11/12
Remaining work = 1 – 11/12 = 1/12
Now, 1/10 of work done by Mohan in 1 day.
Therefore 1/12 of work done by Mohan in 1 day = 10 * 1/12 = 5/6 days
Hence, trench will be dug in = (10 + 5/6) days = 10 5/6 days

7. A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work in ?
a) 15 days
b) 10 days
c) 9 days
d) 8 days
e) none of these
Explanation:
Ratio of times taken by A and B = 1:3
Means B will take 3 times which A will do in 1 time
If difference of time is 2 days, B takes 3 days
If difference of time is 10 days, B takes (3/2) * 10 =15 days

8. A work is done by three person A,B and C. A alone takes 10 hours to complete a single product but B and C working together takes 4 hours, for the completion of the same product. If all of them worked together and completed 14 products, then how many hours have they worked?
a) 20 hrs
b) 28 hrs
c) 40 hrs
d) 54 hrs
e) none of these
Explanation:
1/A=1/10 and
1/B+1/C=1/4 (Given)
1/A+1/B+1/C=1/4+1/10
=7/20
In 20 hours, working together they will complete 7 products.
Thus in 40 hours they will complete 14 products

9. A takes half as long to do a piece of work as B takes, and if C does in the same time as A and B together, and if all three working together would take 7 days, how long would each take separately?
a) 21 days, 42 days, 14 days
b) 20 days, 40 days, 40/3 days
c) 15 days, 45 days, 45/4 days
d) None of these
e) Can’t determine
Explanation:
Let A takes x days to complete the work. Then, B takes 2x days
ATQ, C takes to complete the work = 2x * x/(2x + x) = 2x/3 days
Now, applying the given rule, we have
[x * 2x * (2x/3)]/[(x * 2x) + (2x * 2x/3) + (x * 2x/3)] = 7
=> [(4x^3)/3]/4x^2 = 7 => x/3 = 7 => x = 21 days
Hence A completes the work in 21 days, B takes 42 days and C in (2 * 21/3) = 14 days

10. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?
a) 11:30 A.M.
b) 12 noon
c) 12:30 P.M.
d) 1:00 P.M.
e) None of these 