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# Arithmetic Aptitude :: Time and Work

Home > Arithmetic Aptitude > Time and Work > General Questions

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51. A completes a work in 2 days, B in 4 days, C in 9 and D in 18 days. They form group of two such that difference is maximum between them to complete the work. What is difference in the number of days they complete that work?

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Explanation:

If C and D form a pair and A and B form a pair the difference is maximum.
Now C and D together can complete the work = 9*189+189*189+18 = 6 days.
A and B together can complete the work = 2*42 + 42*42 + 4 = 4/3 days.
Difference = (6 - 4/3) = 14/3 days.

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52. 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?

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Explanation:

A's 1 day work = 1/6
B's 1 day work = 1/8
So, C's 1 day's work = 1/3 - (1/6 + 1/8) = (1/3 - 7/24) = 1/24.
So, A's wages : B's wages : C's wages
=> 1/6 : 1/8 : 1/24 = 4:3:1
So, C's share = (1/8 * 3200) = Rs 400.

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53. Hanuman can complete a bridge in 10 days and Ravanan can complete the same bridge in 20 days. Now they are working together and they are completing the bridge in 20 days. What is the contribution of Ravanan in constructing the bridge?

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Explanation:

Hanuman= 10 days so in 1 day= 1/10
Ravanan = 20 days so in 1 day= 1/20
If Ravanan helps Hanuman then their one day work will be =1/10+1/20= 3/20 so they can complete the bridge in 20/3 days= 6.33 days
But acc. to the question the bridge is constructed in 20 days so its only possible when Ravanan is involved in
destructing the bridge coz (1/10-1/20)= 1/20
hence 20 days required to built the bridge.

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54. Daniel can do some work in 12 hours, Roy can do the same work in 10 hours while Hillari can do the same work in 15 hours. All the three of them start working at 9 a.m while Daniel stops works at 11 a.m and remaining two complete the work. Approximately at what time will the work be finished?

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Explanation:

Daniel= 12 hrs so 1 hr work = 1/12 Similarly Roy= 1/10 and Hillari =1/15
In 1 hr they will do 1/12+1/10+1/15= 1/2 in 1 hr
so in 2 hrs (9 am -11 am) work done is 1/2
Now Daniel stops working so Roy and Hillari work together
1/10+1/15 = 1/6 in 1 hr
So 1 in 6 hr hence 1/2 in 3 hr hence three hours from 11 am they will finish the work that is 2pm.

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55. Aravind can do a work in 24 days. Mani can dig the same well in 36 days. Aravind, Mani and Hari can do a work together in 8 days. Hari alone can do the work in

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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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56. 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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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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57. 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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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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58. The price of a book in four different shops and the successive discounts offered for the books is given below. Select the option in which the price of the book is the least.

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Explanation:

P1=P[1-(d1/100)][1-(d2/100)][1-(d3/100)]...........[1-(dn/100)]
where d1,d2,d3...dn are discount rates
option D satisfy.

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59. 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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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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60. 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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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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