Relationship between work and time

1

If A can finish a work in 10 days and B can finish the same work in 15 days, how many days will they take if they work together?

A. 5 days B. 6 days C. 8 days D. 12 days

Show Answer

✔ Correct: B

A's 1-day work = 1/10. B's 1-day work = 1/15. Together = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Thus, they take 6 days.

2

If 10 men can complete a project in 20 days, how long will it take for 20 men to complete the same project?

A. 10 days B. 20 days C. 40 days D. 5 days

Show Answer

✔ Correct: A

Using M1D1 = M2D2, 10 * 20 = 20 * D2, which gives D2 = 10 days.

3

Two pipes A and B can fill a tank in 12 and 16 hours respectively. If both are opened together, how long will they take to fill the tank?

A. 6.85 hours B. 7.5 hours C. 8.25 hours D. 9 hours

Show Answer

✔ Correct: A

Work = 1/12 + 1/16 = 4/48 + 3/48 = 7/48. Time = 48/7 = 6.857 hours.

1

Assertion (A): If the number of workers is increased, the time taken to complete the job decreases, assuming the rate of work per person remains constant.
Reason (R): Work done is inversely proportional to the time taken when the number of workers varies.

Directions: Choose the correct option:
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is not the correct explanation of A.
(C) A is true but R is false.
(D) A is false but R is true.

A. Option A B. Option B C. Option C D. Option D

Show Answer

✔ Correct: A

Both Assertion and Reason are true, and the Reason correctly explains the Assertion.

2

Assertion (A): If A completes 1/x of a work in 1 day, then A takes x days to complete the work.
Reason (R): The total work is always considered as 0.

Directions: Choose the correct option:
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is not the correct explanation of A.
(C) A is true but R is false.
(D) A is false but R is true.

A. Option A B. Option B C. Option C D. Option D

Show Answer

✔ Correct: C

Assertion is true, but Reason is false because total work is considered as 1 unit, not 0.

1

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?

Show Answer & Solution

Let B's 1-day work = x, then A's 1-day work = 2x. Together (x + 2x) = 3x = 1/18. So x = 1/54. B takes 54 days, A takes 27 days.

2

Calculate the time taken if 5 machines can produce 5 items in 5 minutes.

Show Answer & Solution

Using M1D1/W1 = M2D2/W2, 5*5/5 = 1*D2/1. D2 = 5. So, 1 machine takes 5 minutes to produce 1 item.

1

A, B, and C can do a piece of work in 20, 30, and 60 days respectively. How long will it take for A to complete the work if he is assisted by B and C on every third day?

Show Answer & Solution

Step 1: A's 1-day work = 1/20, B's = 1/30, C's = 1/60. Step 2: Work in first two days = 2 * (1/20) = 1/10. Step 3: Work on third day = 1/20 + 1/30 + 1/60 = (3+2+1)/60 = 6/60 = 1/10. Step 4: Total work in 3 days = 1/10 + 1/10 = 1/5. Step 5: Total time = 3 * 5 = 15 days.

2

A contractor undertook to complete a project in 90 days and employed 60 men. After 60 days, only 3/4 of the work was completed. How many additional men should he employ to finish the work on time?

Show Answer & Solution

Step 1: Work done in 60 days by 60 men is 3/4. Step 2: Remaining work = 1/4. Remaining time = 90 - 60 = 30 days. Step 3: Use formula (M1 * D1) / W1 = (M2 * D2) / W2. (60 * 60) / (3/4) = (M2 * 30) / (1/4). Step 4: 3600 / (3/4) = (M2 * 30) / (1/4) => 4800 = M2 * 120. M2 = 40. Since he needs 40 men total, he needs to employ 40 men total, but he already has 60? Calculation check: If 60*60 / 0.75 = 4800. M2*30 / 0.25 = M2*120. M2 = 40. He already has 60 men, so he needs 0 additional men as 60 is more than 40.

1

Case Study: A construction company is building a bridge. It is observed that 12 workers can build the foundation in 20 days. Due to an urgent deadline, the manager wants to finish the work in 15 days.

Sub-question 1: How many total workers are required to finish the work in 15 days?

Show Solution

Using M1D1 = M2D2, 12 * 20 = M2 * 15. M2 = 240 / 15 = 16 workers.

Sub-question 2: How many additional workers must be hired?

Show Solution

Additional workers = 16 - 12 = 4 workers.

The Concept of Unit Work

Efficiency and Work Relationship

Section A: Multiple Choice Questions (MCQs)

Section B: Assertion-Reason Questions

Section C: Short Answer Questions

Section D: Long Answer Questions

Section E: Case-Based Questions

Dynamic Test Generator (Gemini Powered)