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
Answer: A)
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
Answer: D)
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
Answer: B)
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
Answer: C)
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
Answer: A)
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
Answer: B)
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
Answer: A)
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
Answer: C)
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
Answer: A)
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
Answer: D)
Explanation:
