41.  A and B can together finish a work in 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 job?

40
50
54
60

```Answer

Answer: Option  D Explanation:(A+B)'s 20 days work = (1/30*20) = 2/3. Remaining work = (1- 2/3) = 1/3.
Now, 1/3 work is done by A in 20 days.
Whole work will be done by A in (20*3) = 60 days. ```

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42.  A and B can do a work in 12 days, B and C in 15 days, C and A in 20 days. If A, B and C work together, they will complete the work in

5 days
7 5/6 days
10 days
15 2/3 days

```Answer

Answer: Option  C Explanation:(A+B)' s 1 day's work = 1/12; (B+C)'s 1 day's work = 1/ 15; (A+ C)'s 1 day's work = 1/20.
Adding, we get : 2 (A+B+C)'s 1 day's work = (1/12+1/15+1/20) = 12/60 = 1/5.
therefore (A+B+C)'s 1 day's work = 1/10.
so A,B and C together can complete the work in 10 days. ```

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43.  A and B can do a piece of work in 72 days; B and C can do it in 120 days; A and C can do it in 90 days.In what time can A alone do it/

80 days
100 days
120 days
150 days

```Answer

Answer: Option  C Explanation:(A+B)'s 1 day's work = 1/72; (B+C)'s 1 day's work = 1/120; (A+C)'s 1 day's work = 1/90.
Adding, we get : 2 (A+B+C)'s 1 day's work = (1/72+1/120+1/90) = 12/360 = 1/30.
= (A+B+C)'s 1 day's work = 1/60.
so, A's 1 day's work = (1/60 - 1/120) = 1/120.
therefore A alone can do the work in 120 days. ```

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44.  A and B can do a piece of work in 5 days; B and C can do it in 7 days; A and C can do it in 4 days. who among these will take the least time if put to do it alone?

B
C
A

```Answer

Answer: Option  C Explanation:(A+B)'s 1 day's work = 1/5; (B+C)'s 1 day's work = 1/7; (A+C)'s 1 day's work =1/4.
Adding, we get : 2 (A + B + C) 's 1 day's work = (1/5 + 1/7 + 1/4) = 83/140.
(A+B+C)'s 1 day's work = 83/280.
A's 1 day's work = (83/280 - 1/7) = 43/280; B's 1 day's work = (83/280 - 1/4) = 13/280;
C's 1 day's work = (83/280 - 1/5) =27/280.
Thus time taken by A,B,C is 280/43 day's, 280/13 day's, 280/27 days respectively.
Clearly, the time taken by A is least. ```

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45.  A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

18 days
24 days
30 days
36 days

```Answer

Answer: Option  A Explanation:2(A+B+C)'s 1 day's work = (1/30+1/24+1/20) = 15/120 = 1/8.
= (A+B+C)'s 1 day's work =1/16.
Work done by A,B and C in 10 days = 10/16 = 5/8. Remaining work = (1- 5/8) = 3/8.
A's 1 day's work = (1/16 - 1/24) = 1/48.
Now, 1/48 work is done by A in 1 day.
so, 3/8 work will be done by A in (48*3/8) = 18 days. ```

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