Time & Work (1)

1. P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
1. 8/15
2. 7/15
3. 11/15
4. 2/11

Answer & Explanation

Answer:- 1

Explanation :-

P’s 1 day Work = 1/15,         Q’s 1 day Work = 1/20
1 day Work of both P & Q together = (1/15) + (1/20) = 7/60
Work that P & Q  together do in 4 days = 4 * (7/60) = 7/15
Work left = 1 – 7/15= 8/15

 

2. P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
1. 9(3/5) days
2. 9(1/5) days
3. 9(2/5) days
4. 10 days

Answer & Explanation

Answer:- 1

Explanation :-

P’s 1 day Work = 1/12,        Q’s 1 day Work = 1/16
Work that P, Q & R can together do in 1 day = 1/4
R’s 1 day Work = 1/4 – [(1/16) + (1/12)] = [12 -( 4 + 3)] /48= 5/48
Therefore,  R alone can complete the work in 48/5 days = 9 and (3/5) days

 

3. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
1. 10 days
2. 14 days
3. 15 days
4. 9 days

Answer & Explanation

Answer:- 3

Explanation :-

P’s 1 day Work = 1/20,        Q’s 1 day Work = 1/30,       R’s 1 day Work = 1/60
P’s 2 day work = 2*(1/20) = 1/10
At every third day they work together, therefore
Work done by  P,Q & R at every third day = (1/20) + (1/30) + (1/60) = 1/10
Work done in 3 days = (1/10) + (1/10) = 1/5
Whole work will be done in = (3 x 5) = 15 days.

 

4. A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in – days if they work together.
1. 18 days
2. 22 ½ days
3. 24 days
4. 26 days

Answer & Explanation

Answer:- 2

Explanation :-

Let A can complete the work in x days ,
Therefore, B can complete the same work in 3x days
3x – x = 60 days, therefore,   x = 30 days   3x = 90 days
A’s 1 day Work = 1/30,        B’s 1 day Work = 1/90,
Work that A & B  together do in 1 days = (1/30) + (1/90) = 2/45
Therefore, A & B together can do the work in 45/2 days = 22 ½ days

 

5. A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
1. Rs. 380
2. Rs. 600
3. Rs. 420
4. Rs. 400

Answer & Explanation

Answer:- 4

Explanation :-

A’s 1 day Work = 1/6,        Q’s 1 day Work = 1/8
Work that P, Q & R can together do in 1 day = 1/3
C’s 1 day Work = 1/3 – [(1/6) + (1/8)] = [8 – (4 + 3)]/24 = 1/24
A’s 1 day Work : B’s 1 day Work : C’s 1 day Work
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount paid to C = (3200/8) × (1) = 400

 

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