Time and Work :(96) MCQs with Answers

1.

Pramodh can complete a work in 18 days. Prasad completes the same work in 24 days. They both started the work Prasad left the work after some days. Pramodh completed the remaining work in 11 days. Then after how many days Prasad left the work? 

   A.) After 3 days
   B.) After 4 days
   C.) After 5 days
   D.) After 6 days

Answer: Option 'B'

(x/18) + (x/24) + (11/18) = 1
(x/18) + (x/24) = 1 - (11/18)
(4x + 3x)/72 = (18 - 11)/18
7x/72 = 7/18
x = 4
After 4 days

2.

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 the work. Approximately at what time will the work be finished?

   A.) 11: 30 a.m.
   B.) 12 noon
   C.) 12:30 p.m
   D.) 1 p.m.

Answer: Option 'D'

The three machines 1 hour’s work = 1/8 + 1/10 + 1/12 = 37/120
Their, work from 9 a.m. to 11 a.m. = 2 hour’s work = 37/120 × 2= 27/60 
The remaining work = 23/60 
Machines Q and R’s 1 hours work = 1/10 + 1/12 = 11/60 
Therefore, the time taken by Q and R to finish the remaining 23/60 work = 23/60/11/60 
= 23/60 × 60/11 = 23/11 = 2 hours approx. 
Therefore, the approximate time at which the work is finished = 11 + 2 = 1 p.m.

3.

If A, B and C can do a job in 20, 30 and 60 days respectively. In how many days A can do the work if B and C help him on every third day?

   A.) 12 days
   B.) 15 days
   C.) 16 days
   D.) 18 days

Answer: Option 'B'

Efficiency of A = 1/20 = 5% per day
Efficiency of B = 1/30 = 3.33% per day
Efficiency of C = 1/60 = 1.66% per day
In three days A can do 15% of the job himself and B and C do 5% of the job ( 1.66% + 3.33% )
In three days they can do 20% of the job, to do 100% of the job, they need 3 × 5 = 15 days

4.

Kamal can do a work in 15 days. Bimal is 50% more efficient than Kamal. The number of days, Bimal will take to do the same piece of work, is 

   A.) 10
   B.) 10 ½
   C.) 12
   D.) 14

Answer: Option 'A'

Kamal’s 15 days is 150% of No. days taken by Bimal to finish the job.
Therefore, the No. of days taken by Bimal = 15/150 × 100 = 10 days

5.

A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work is: 

   A.) 11
   B.) 21
   C.) 28
   D.) 42

Answer: Option 'B'

A’s work is twice as B’s work 
So, we can consider 2A = B 
Then, A × 2A/ A+ 2A = 14 
2A × A/ 3A = 14 
2 A = 14 × 3 
A = 21 days. i.e. A alone can finish the work in 21 days.

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