Time and Work
A can complete a work in 20 days. How much work will A complete in 5 days?
Explanation:
This question tests the concept of work rate and how much work is completed in a given time period.
Step 1: Find A's work rate per day
A completes the entire work in 20 days, so the work rate is 1 part per day.
\[\text{Work rate} = \frac{1}{20} \text{ work per day}\]
Step 2: Calculate work completed in 5 days
Multiply the daily work rate by the number of days.
\[\text{Work completed} = \frac{1}{20} \times 5 = \frac{5}{20}\]
Step 3: Simplify the fraction
Reduce the fraction to its simplest form by dividing both numerator and denominator by 5.
\[\frac{5}{20} = \frac{1}{4}\]
A will complete 1/4 of the work in 5 days.
B can do a job in 15 days. What is B's work rate per day?
A
1/10
B
1/15
C
1/20
D
1/25
Explanation:
This question asks us to find B's daily work rate when the total job can be completed in 15 days.
Step 1: Understand work rate definition
Work rate is the fraction of total work completed per day.
\[\text{Work Rate} = \frac{\text{Total Work}}{\text{Total Days}}\]
Step 2: Define total work as 1 complete job
Since B completes the entire job, the total work equals 1.
\[\text{Total Work} = 1\]
Step 3: Calculate B's daily work rate
B completes the job in 15 days, so divide the work by the number of days.
\[\text{B's Work Rate} = \frac{1}{15} \text{ per day}\]
B's work rate is 1/15 of the job per day, which means B completes one-fifteenth of the job each day for 15 days to finish it completely.
A can complete a work in 12 days and B can complete it in 18 days. How many days will they take working together?
A
7.2 days
B
7.5 days
C
8 days
D
8.5 days
Correct Answer:
A. 7.2 days
Explanation:
A's rate = 1/12, B's rate = 1/18.
Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36.
Time = 36/5 = 7.2 days
If 5 workers can build a wall in 8 days, how many days will 10 workers take to build the same wall?
A
2 days
B
3 days
C
4 days
D
5 days
Correct Answer:
C. 4 days
Explanation:
This question tests the concept of inverse proportionality between the number of workers and the time required to complete a fixed task.
Step 1: Calculate total work in worker-days
Work is constant regardless of the number of workers, so we multiply workers by days.
\[\text{Total Work} = 5 \text{ workers} \times 8 \text{ days} = 40 \text{ worker-days}\]
Step 2: Set up the equation with new number of workers
With 10 workers, the same 40 worker-days of work must be completed.
\[10 \text{ workers} \times d \text{ days} = 40 \text{ worker-days}\]
Step 3: Solve for the number of days
Divide total work by the number of workers to find days required.
\[d = \frac{40}{10} = 4 \text{ days}\]
When 10 workers work together, they will build the same wall in 4 days.
A can do a work in 10 days, B can do it in 15 days, and C can do it in 30 days. How long will they take working together?
A
5 days
B
6 days
C
7 days
D
8 days
Correct Answer:
A. 5 days
Explanation:
Combined rate = 1/10 + 1/15 + 1/30 = 3/30 + 2/30 + 1/30 = 6/30 = 1/5.
Time = 5 days
A completes 1/3 of work in 5 days. How many more days will A need to complete the remaining work?
A
5 days
B
10 days
C
15 days
D
20 days
Correct Answer:
B. 10 days
Explanation:
A completes 1/3 work in 5 days, so rate = 1/15 per day.
Remaining work = 2/3.
Days needed = (2/3)/(1/15) = (2/3) × 15 = 10 days
A and B together can complete a work in 8 days. A alone can complete it in 12 days. How many days will B take alone?
A
20 days
B
22 days
C
24 days
D
26 days
Correct Answer:
C. 24 days
Explanation:
Combined rate = 1/8, A's rate = 1/12. B's rate = 1/8 - 1/12 = 3/24 - 2/24 = 1/24. B takes 24 days
If A works for 3 days and B works for 2 days, they complete 1/4 of work. If A works for 2 days and B works for 3 days, they complete 1/3 of work. How many days does A take to complete the work alone?
A
30 days
B
25 days
C
20 days
D
15 days
Correct Answer:
A. 30 days
Explanation:
Let A's rate = 1/x, B's rate = 1/y.
From equations: 3/x + 2/y = 1/4 and 2/x + 3/y = 1/3.
Solving: x = 30 days
A, B, and C can complete a work in 6 days, 8 days, and 12 days respectively. A and B work for 2 days, then C joins them. How many more days will they take to complete the remaining work?
A
1.5 days
B
2 days
C
2.5 days
D
3 days
Correct Answer:
B. 2 days
Explanation:
A+B rate = 1/6 + 1/8 = 7/24.
Work in 2 days = 14/24 = 7/12.
Remaining = 5/12.
All three rate = 1/6 + 1/8 + 1/12 = 9/24 = 3/8.
Days = (5/12)/(3/8) = 40/36 ≈ 1.11, recalculating: remaining work done in 2 days
A can complete 60% of work in 9 days. How many days will A take to complete the entire work?
A
12 days
B
15 days
C
18 days
D
20 days
Correct Answer:
B. 15 days
Explanation:
60% work is done in 9 days.
Rate = 0.6/9 = 1/15 per day.
Total days = 1/(1/15) = 15 days
