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# Arithmetic Aptitude :: Time and Work

Home > Arithmetic Aptitude > Time and Work > General Questions

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81. A,B ,C can do some work in 36 days. A and B together do twice as much work as C can do alone, and A and C together can do thrice as much work as B alone can do. Find the time taken by C to do whole work?

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Explanation:

Given A, B and C can do some work = 36 days.

=> (A+B+C) can do work in 1 day = 1/36
=> (A+B+C) = 1/36 -----------------(i)
Given (A+B) = 2C ----------------(ii)

From eq. (i)and(ii)
3C = 1/36
C = 1/108

=> C takes 108 days to complete whole work alone.

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82. X takes 4 days to complete one-third of a job,Y takes 3 days to complete one-sixth of the same work and Z takes 5 days to complete half the job.If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.

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Explanation:

X completes 1/3rd in 4 days = 33.33 % job in 4 days.
X One day work = 8.33%
Y one day work = 5.55% [As he complete 1/6 job = 16.66 % job in 3 days]
Z one day work = 10%
Work done in 3 days by X, Y and Z
= 25 + 16.66 + 30 = 71.66 %
Remaining work will be done by Y in,
28.33/5.55 = 5.1 days.

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83. A certain sum of money is sufficient to pay either George's wages for 15 days or Mark's wages for 10 days. For how long will it suffice if both George and Mark work together?

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Explanation:

Let the money to be paid = 30 rupees.
So, George daily wage = 30/15 = 2
and Mark daily wage = 30/10 = 3.
If both are working,
then 5 rupees to be paid.
So given sum is sufficient for 30 / 5 = 6 days.

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84. A and B can do a piece of work in 40 days. Thier skills of doing the work are in the ratio 8:5. how many days will A take to engage alone ?

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Explanation:

Ratio of efficiency of A:B=8:5
Total Efficiency=13
They complete the work in 40 days
When the efficiency of A is 8
A could complete the work in (40/8)*13=65 days
Thus. A alone can do the work in 65 days

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85. A alone can do 1/4th of the work in 2 days. B alone can do 2/3th of the work in 4 days. If all the three work together, they can complete it in 3 days so what part of the work will be completed by C in 2 days?

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Explanation:

A can do the total work in 8 days, and B can do it in 6 days.
Let the total work be 24 units. Now capacities are
A = 24/8 = 3,
B = 24/6 = 4,
A + B + C = 24/3 = 8
So Capacity of C = 1 unit.
In two days C will do 2 units which is 2/24th part of the total work. So 1/12th part.

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86. George and Mark can paint 720 boxes in 20 days, Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is

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Explanation:

Capacities of these people as followes
G + M = 720/20 = 36
M + H = 720/24 = 30
H + G = 720/15 = 48
Adding all above we get 2(G + M + H ) = 114 => G + M + H = 114/2 = 57
Now individual capacities are given below
G = 27 ; M = 9; H = 21
So 27 * 4 + 9 * 8 + 21 * 8 = 348

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87. 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:

Let man daily wages and woman daily wages be M and W respectively 24M+16W=11600
12M+37W=11600

By, solving the above equations gives M=350 and W=200

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88. Thomas takes 7 days to paint a house completely whereas Raj would require 9 days to paint the same house completely. How many days will take to paint the house if both them work together. (Give answers to the nearest integer)?

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Explanation:

Thomas=7 days. so 1 day work is 1/7
Raj= 9 days= so 1 day work is 1/9
Hence if both work together for 1 day they will do 1/7+ 1/9= 16/63
So 16/63 in 1 day
So 1 in 63/16 day i.e approx.=4days

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89. Rajiv can do a piece of work in 10 days , Venky in 12 days and Ravi in 15 days. They all start the work together, but Rajiv leaves after 2 days and Venky leaves 3 days before the work is completed. In how many days is the work completed?

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Explanation:

Let the work be 60 units. If venky leave 3 days before the work, Last 3 days must be worked by Ravi.
So the remaining days of work be x days,
Total days to complete the work be x + 3 days.

Now Capacities of Rajiv is 60/10 = 6,
Venky is 5,
Ravi is 4. (6 + 5 + 4) 2 + (5 + 4) (x - 3) + 4 x 3 = 60.

30 + 9x - 27 + 12 = 60 9x - 15 =30

9x = 45 x = 5

So total days to complete the work = 2 + 5 = 7 days.

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90. Babla alone can do a piece of work in 10 days. Ashu alone can do it in 15 days. The total wages for the work is Rs.5000. How much should be Babla be paid if they work together for an entire duration of work.

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