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# Arithmetic Aptitude :: Time and Work

Home > Arithmetic Aptitude > Time and Work > General Questions

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41. Amit want to make a 1000 m long wall with in 50 days he made a decision to hire 56 man however after 27 days amit realized that team was only able to make 448 meter wall find out the additional number of man that amit should employ as a mean of finishing work on the stipulated time.

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Explanation:

It take 56*27 = 1512 labour to complete 448 m .
Therefoe labour required to complete 1m = 3.375.
Now labour required to complete remaining 552 m =552*3.375 =1863 and days remaining is 23.
So labours required in one day =1863/23=81.

So additional labours required is = 81- 56 = 25.

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42. 2 computers each produced 48000 public utility bills in a day. One computer printed bills at the rate of 9600 an hour and the other at the rate of 7800 an hour. When the first computer finished its run, how many bills did the other computer still have to print?

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Explanation:

48000=9600*Hour
Hour =5

7800*5=39000

48000-39000=9000

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Tags:  Capgemini

43. A group of workers can do a piece of work in 24 days. However as 7 of them were absent it took 30 days to complete the work. How many people actually worked on the job to complete it?

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Explanation:

Let the original number of workers in the group be 'x'
Therefore, actual number of workers = x-7.
We know that the number of manhours required to do the job is the same in both the cases.
Therefore, x (24) = (x-7).30
24x = 30x - 210
6x = 210
x = 35.
So, the actual number of workers who worked to complete the job = x - 7 = 35 -7 = 28.

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44. Two persons A and B working together can dig a trench in 8 hrs while A alone can dig it in 12 hrs. In how many hours B alone can dig such a trench?

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Explanation:

Given (A+B)'s one hours work = 1/8
and A's one hours work =1/12
Therefore, B's one hours work = (1/8-1/12) =1/24.
So, B alone can dig the trench = 24 hours.

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45. X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs. 720. With the help of Z they finished it in 5 days. How much is paid to Z?

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Explanation:

In one day X can finish 1/15 th of the work.
In one day Y can finish 1/10 th of the work.

Let us say that in one day Z can finish 1/Z th of the work.
When all the three work together in one day they can finish 1/15 + 1/10 + 1/Z = 1/5 of the work.
Therefore, 1/Z = 1/30.
Ratio of their efficiencies = 1/15: 1/10: 1/30 = 2: 3: 1.Therefore Z receives 1/6 of the total money.
According to their efficiencies money is divided as 240: 360: 120.
S0, the share of Z = Rs. 120.

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46. A is twice as good a workman as B and together they finish a piece of work in 18 days.In how many days will A alone finish the work?

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Explanation:

Given A is twice as good a workman as B
So (A’s 1 day’s work): (B’s 1 day’s work) = 2:1.
(A + B)’s 1 day’s work = 1/18.
Divide 1/18 in the ratio 2:1.
Therefore A’s 1 day’s work = (1/18 * 2/3) = 1/27.
Hence, A alone can finish the work in 27 days.

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47. A and B can do a piece of work in 12 days ; B and C can do it in 20 days. In how many days will A, B and C finishes it working all together? Also, find the number of days taken by each to finish it working alone?

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Explanation:

Given (A+B)’s one day’s work=1/12 ---- (1)
(B+C)’s one day’s work=1/15 ------- (2)
and (A+C)’s one day’s work=1/20. -------- (3)
By eq. 1, 2 and 3
2(A+B+C)’s one day’s work = (1/12+1/15+1/20)=1/5.
=> (A+B+C)’s one day’s work=1/10.
=> A, B and C together can finish the work in 10 days.
Now, A’s one day’s work
= [(A+B+C)’s one day’s work] – [(B+C)’s one day’s work]
= 1/10-1/15)
= 1/30.
Therefore, A alone can finish the work in 30 days.
Similarly, B’s 1 day’s work = (1/10 -1/20) = 1/20.
Therefore, B alone can finish the work in 20 days.
And, C’s 1 day’s work= (1/10-1/12) = 1/60.
Therefore, C alone can finish the work in 60 days.

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48. 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?

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Explanation:

Lets assume 1 man’s 1 day’s work = x
and 1 boy’s 1 day’s work = y.
=> 2x+3y=1/10 ---- (1)
and 3x+2y=1/8. ----- (2)
By Solving eq. (1) and (2)
x=7/200 and y=1/100.
Therefore (2 men +1 boy)’s 1 day’s work = (2*7/200 + 1*1/100) = 16/200 = 2/25.
So, 2 men and 1 boy together can finish the work in 25/2 =12 1/2 days.

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49. Jake can dig a well in 16 days. Paul can dig the same well in 24 days. Jake, Paul and Hari together dig the well in 8 days. Hari alone can dig the well in ?

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Explanation:

As Jake , Paul and Hari can dig the well in 8 days,
Jack one day work = 1/16
Paul one day work = 1/24
Given, (Jake,Paul and hari) 1 day work = 1/8

So, 1/16 + 1/24 + 1/x = 1/8

=> 1/x=1/48

Therefore, Paul can finished work in 48 days.

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ShortCut

50. 15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 6 hrs. each would it take for 21 women if 3 women do as much work as 2 men?

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Explanation:

15 men - 8hrs - 21 days ( Its given 3 women = 2 men so 21 women= 14 men)
15 men - 1 hr - 21*8days
1 man - 1 hr - 21*8*15 days =2520 days
1 man - 6 hours - 2520/6 days
14 men - 6 hours - 2520/(14*6)= 30 days

ShortCut By :: BACHU VENKATA THARUN KUMAR

(15)(21)(8)=(6)(21/3)*2(x)

x=30

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