__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:**