RRB NTPC - Time and Work :(96) MCQs with Answers

1.

A can do a piece of work in 12 days, while B can do it in 8 days with the help of C, they finish the work in 4 days. Then C alone can do the work in 

   A.) 24 days
   B.) 20 days
   C.) 16 days
   D.) 4 days

Answer: Option 'A'

A and B together can do the work in 12 × 8/20 = 96/20 days 
A +B and C together do the work in 4 days. 
Then C alone can do the work in 96/20 × 4/96/20 – 4 days 
= 96/5/16/20 = 96/5 × 20/16 = 24 days.

2.

Raju can complete a work in 30 days. Ajay completes the same work in 20 days. They both started the work Raju left the work after some days. Ajay completed the remaining work in 15 days. Then after how many days Raju left the work?

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

Answer: Option 'C'

(x/30) + (x/20) + (15/20) = 1
(2x + 3x)/60 = 1 - (15/20)
5x/60 = (20 - 15)/20
5x/60 = 5/20 
x/3  = 1
x = 3 days
After 3 days

3.

A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day? 

   A.) 1/6
   B.) 1/9
   C.) 2/5
   D.) 2/7

Answer: Option 'A'

B alone can do the same work in 9 days 
So, the No. of days both of them together take to do the work = 18 × 9/ 18 + 9 
=18 × 9/27 = 6 days. 
The part of the work, they together finish in one day = 1/6.

4.

Vamsi and Vivek can complete a piece of work in 30 and 15 days repectively by working alone. After how many days 80% of the work would have got completed? 

   A.) 8 days
   B.) 12 days
   C.) 14 days
   D.) 10 days

Answer: Option 'A'

Let the time taken by Vamsi = A days = 30 days
the time taken by Vivek = B days = 15 days

Vamsi + Vivek together can complete 100 % of the work in:
=> 1/(A + B) = (1/A) + (1/B)
=> 1 / (A + B) = (1 / 30) + (1 / 15)
=> 1 / (A + B) = (15 + 30) / (30 * 15)
=> 1 / (A + B) = 45 / 450
Taking reciprocal on both sides
A + B = 450/45
A + B = 10 days

Thus 100% of the work is completed in 10 days,
80% of the work is completed in {(10 / 100%) × 80%} days = 8 days

5.

A works twice as fast as B. if B can complete a work in 12 days independently. The number of days in which A and B can together finish the work? 

   A.) 18 days
   B.) 8 days
   C.) 6 days
   D.) 4 days

Answer: Option 'D'

If B takes 12 days to finish the work, then A takes 6 days to finish the same work. 
If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. 
Therefore, the Number of days taken by A and B together to finish the same work = 6 × 12/18 
= 4 days.

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