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Arithmetic Aptitude :: Time and Work

Home > Arithmetic Aptitude > Time and Work > General Questions

51. Aravind can dig a well in 24 days. Mani can dig the same well in 36 days. Aravind, Mani and Hari can dig the same well working together in dig the same well working alone in how many days?

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Answer: Option B

Explanation:

Aravind = 24 days so 1 day work =1/24
Mani= 36 days so 1 day work = 1/36
Let Hari can alone do in x days so 1 day work = 1/x
All working together= 1/24+1/36+1/x= 1/8 can complete the work in 8 days
Solving the equation we get x= 18 days.

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52. If twenty four men and sixteen women work on a day, the total wages to be paid is 11,600. If twelve men and thirty seven women work on a day, the total wages to be paid remains the same. What is the wages paid to a man for a day's work?

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Answer: Option B

Explanation:

Lets assume man daily wages and woman daily wages be M and W respectively
24M+16W=11600 ---------(1)
12M+37W=11600 ---------(2)
By solving above eq. (1) and (2)
M=350 and W=200

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53. A takes 2 hours to make a publication. B takes 10 hours to make a publication. Find the time taken by them to make two publications, working independently.

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Answer: Option A

Explanation:

A completes one publication ====> 12 hours
B completes one publication ====> 10 hours
So, the maximum time taken to complete these two publications is 12 hour.

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54. There are 3 trucks A,B and C. A loads at the rate of 10kg/min and B loads at the rate of 13 1/3 kg/min. C unloads at the rate of 5kg/min. If all the 3 trucks are acting simultaneously, find the time taken to load 2.4 tonnes.

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Answer: Option B

Explanation:

A loads in 1 min = 10 kg.
B loads in 1 min = 13 1/3 kg = 40/3 kg.
C unloads in 1 min = 5kg.

So 10+ 40/3 -5 = 55/3

Hence 1 kg loaded by A,B and C together = 3/55 min

So for 2.4 tonnes to be loaded = 2.4 *1000* 3/55 =130.9 min

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55. A can complete a piece of work in 8 hours, B can complete in 10 hours and C in 12 hours. If A,B, C start the work together but A laves after 2 hours. Find the time taken by B and C to complete the remaining work.

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Answer: Option A

Explanation:

A,B,C 1 hour work is=1/8+1/10+12= 37/120
A,B,C work together for 2 hours, so,A,B,C 2 hours work is: (37/120)*2=37/60
remaining work=1-37/60=23/60 (23/60 work is done by B and C together)
B,C 1 hour work is= 1/10+1/12=11/60
23/60 hours work done by B,C= (11/60)* (60/23)=11/23
So B & C and complete the remaining work = 2 1/11 days.

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56. A can do a work in 6 days , B can do a work in 8 days and C can do it in 12 days. B left work after 6 days. For how many number of days should A and C should work together to complete the remaining work ?

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Answer: Option A

Explanation:

A complete work in 6 days
B complete work in 8days
C complete work in 12 days
B's 1 day work=1/8
6 day's work=6/8
remaining work=1-6/8=2/8=1/4
A+C 1 day work together = 1/6+1/12=1/4
so A and C work 1 day to complete remaining work

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57. A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?

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Answer: Option C

Explanation:

A can do in 20 days so 1 day work = 1/20.
Let B alone can do in x days so 1 day work of B is = 1/x
Acc. to the question= 1/20+1/x= 1/12
We get x= 15 days.
So B alone can do the whole work doing alone in 15 days.
But Acc. to the question he only does half a work daily so he will take 30 days to complete the full work
If B works together with A then
1/30+ 1/20= 1/15 or 15 days will be taken to complete the work.

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58. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

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Answer: Option D

Explanation:

5 women's 1 day work=1/14
ans= 1/14 + 1/14
= 1/7 units of work
so 7 days

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59. A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?

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Answer: Option D

Explanation:

(A + B)'s 20 day's work = ( 1/30 x 20 ) = 2/3 .
Remaining work = ( 1 - 2/3 ) = 1/3
Now, 1/3 work is done by A in 20 days.
Therefore, the whole work will be done by A in (20 x 3) = 60 days.

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60. Sixteen men can complete a work in twelve days. Twenty four children can complete the same work in 18 days. 12 men and 8 children started working and after eight days three more children joined them. How many days will they now take to complete the remaining work?

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Answer: Option B

Explanation:

Lets assume Men as "M" and children as "C" .
So as per the Question
16M*12 = 24C*18
=> M/C=9/4
Total work= 16*9*12
Lets assume days required to complete remaining work = x days.
(12*9+8*4)*8+(12*9+11*4)*x=16*9*12
x=608//152 = 4 days.

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