Aptitude question and answer on Time and work

In this section we are going to discuss about time and work problems. Not just the overview of the topic, but also you are going to learn the important formulas on time and work along with explanation which is easy to understand.

1

Rambabu can do a piece of work in 5 days and santosh can do the same work in 7 days. if both work together, they will finish the work in 

A.    12 Days
B.    2 Days
C.    \(2{11 \over 12} \) Days
D.    \({12 \over 35} \) Days

Answer : C.  \(2{11 \over 12} \) Days

Explanation:
\({5 \times 7 \over 5 + 7} = {35 \over 12 } =2{11 \over 12} \) days

2

Rajan can do a piece of work in 10 days, Rakesh can do in 12 days and Santosh do the same work in 15 days.In how many days they can finish the work, working together ?

A.    3 days
B.    5 days
C.    4 days
D.    2 days

Answer : C.  4 days

Explanation:

\({1 \over 10}+{1 \over 12}+{1 \over 15}= {6+5+4 \over 60}= {1 \over 4 }\)


3

Sohan and Rohan can do a piece of work in 10 days, Rohan and mohan can do in 12 days, sohan and Mohan in 15 daus. The time taken by them to do this work together is

A.    16 days
B.    15 days
C.    12 days
D.    8 days

Answer : D.  8 days

Explanation:

(S+R)'s 1 days work =\(1 \over 10\)

(R+M)'s 1 days work = \(1 \over 12\)

(M+S)'s 1 days work = \(1 \over 15\)

2(S+R+M)'s 1 day work =\(1 \over 4\)

\(\dot{..}\)(S+R+M)'s 1 day work =\(1 \over 8\)

\(\dot{..}\)Time taken by them to do this together = 8 days


4

Sunil and santosh together can finish a work in 30 days.They worked it for 20 days and then santosh left. The remaining work was done by sunil alone in 20 more days, Santosh alone can finish the work in 

A.    52 days
B.    30 days
C.    48 days
D.    60 days

Answer : D.  60 days

Explanation:

After 20 days, Balance work = \(1 \over 3\)

\(\dot{..}\)     \(20\,x= {1 \over 3 }\)  or   \(x= {1 \over 60 }\)

Again \(x+y={1 \over 30 }\)  or  \({1 \over 60}+y= {1 \over 30}\)

\(\dot{..}\)    \(y= {1 \over 60 }\)


5

Rambabu,Santosh and Sunil can finish a piece of work in 10, 12 and 15 days respectively. If Santosh stops doing the work after 2 days, Rambabu and Sunil will finish the work in  

A.    2 days
B.    3 days
C.    \(2{1 \over 2}\) days
D.    \(3{1 \over 2}\) days

Answer : B.   3 days

Explanation:

\(2(R_b+S_A+S_L)=2\bigg({1 \over 10}+{1 \over 12}+{1 \over 15} \bigg )={1 \over 2}\)

Balance work to be done by \(R_b\) and \(S_L\) = \(1-{1 \over 2}={1 \over 2}\)

\((R_b+S_L)'s \; \; 1 \; day \; work={1 \over 10 }+ {1 \over 15 }= {3+2 \over 30}= {1 \over 6 }\)

\(\dot{..}\) \((R_b+S_L)\) will take 3 Days to do \(1 \over 2 \) of the work


6

Three taps A,B and C can fill a tank in 12,15 and 20 hours respectivvely. If A is open all the time and B and C are opened for one hour each alternatively, and A and B initiate , then tank will will in 

A.    \(7 {3 \over 4}\) hours
B.    8 hours
C.    7 hours
D.    \(7 {1 \over 2}\) hours

Answer : C.  7 hours

Explanation:



7
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C ?
A.    375
B.    800
C.    400
D.    600

Answer : C.  400

Explanation:
C's 1 day's work = \({1\over 3} -\Bigg({1\over 2}+{1\over 8 } \Bigg )= {1\over3}-{7\over 24}={1\over 24 }\)
A's wages : B's wages : C's wages = \({1\over 6}: {1\over 8}:{1\over 24}= 4 : 3:1\)

So, C's share (for 3days) = Rs. \(\Bigg( 3 \times {1 \over 24 } \times 3200 \Bigg) = Rs. 400\)

8
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A.    12 Days
B.    15 Days
C.    16 Days
D.    18 Days

Answer : B.   15 Days

Explanation:
A's 2 day's work = \(\bigg( {1\over 20} \times 2 \bigg )= {1\over 10}\)
(A+B+C)'s 1 day's work = \(\Bigg ( {1 \over 20 }+{1 \over 30 }+{1 \over 60 } \Bigg )={6 \over60}= {1 \over 5 }\)
Work done in 3 days = \(\Bigg( {1\over 10}+{1\over 10} \Bigg)={1\over 5}\)
Now, \({1\over 5}\) work will be done in \((3 \times 5)\) = 15 Days