Time and Workसमय और कार्य questions and answersप्रश्न और उत्तर

How time and work worksसमय और कार्य को समझिए

Take the total work as the LCM of the given days. Then each person’s efficiency is a whole number of units per day, and everything else is simple division.

People working together add their efficiencies. Someone who undoes work (like a leak) has a negative efficiency.

When more people, days or hours are involved, use the M × D × H relation: more people need fewer days for the same work.

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

1. Example 1उदाहरण 1 · Time and work: two people together · Easyआसान

   Arjun can paint a house in 24 days and Meera can paint it in 12 days. Working together, in how many days will they finish it?

   1. 6 days
   2. 7 days
   3. 8 days
   4. 10 days
   Answer:उत्तर: 8 days

   1. Total work = 24 units.
   2. Together per day = 1 + 2 = 3 units.
   3. Days = 24 ÷ 3 = 8.

2. Example 2उदाहरण 2 · Two people working on alternate days · Easyआसान

   A can do a piece of work in 5 days and B in 10 days. They work on alternate days, A starting. In how many days is the work finished?

   1. 6 1/2 days
   2. 3 1/3 days
   3. 7 days
   4. 6 2/3 days
   Answer:उत्तर: 6 1/2 days

   1. Total work = 10 units; A = 2/day, B = 1/day; a two-day cycle = 3 units.
   2. 3 full cycles (6 days) do 9 units, leaving 1.
   3. A works next and the rest is finished on the following day(s): total 6 1/2 days.

3. Example 3उदाहरण 3 · Men, days, hours and work (chain rule) · Easyआसान

   6 workers, working 10 hours a day, finish the wall in 15 days. How many days will 10 workers take to finish the wall, working 10 hours a day?

   1. 9 days
   2. 10 days
   3. 25 days
   4. 11 days
   Answer:उत्तर: 9 days

   1. M₁D₁H₁/W₁ = 6 × 15 × 10 / 1 = 900 worker-hours per unit.
   2. D₂ = 6 × 15 × 10 × 1 / (10 × 10 × 1).
   3. D₂ = 900 / 100 = 9 days.

4. Example 4उदाहरण 4 · Time and work: two people together · Mediumमध्यम

   Aditya and Isha together can complete a project in 14 days. Aditya alone can complete it in 21 days. In how many days can Isha alone complete it?

   1. 34 days
   2. 38 days
   3. 42 days
   4. 53 days
   Answer:उत्तर: 42 days

   1. Work = 42 units. Together = 3/day, Aditya = 2/day.
   2. Isha = 1 units/day.
   3. Isha alone = 42 ÷ 1 = 42 days.

5. Example 5उदाहरण 5 · Two people working on alternate days · Mediumमध्यम

   A can do a piece of work in 12 days and B in 14 days. They work on alternate days, A starting. In how many days is the work finished?

   1. 6 6/13 days
   2. 13 days
   3. 12 12/13 days
   4. 12 6/7 days
   Answer:उत्तर: 12 6/7 days

   1. Total work = 84 units; A = 7/day, B = 6/day; a two-day cycle = 13 units.
   2. 6 full cycles (12 days) do 78 units, leaving 6.
   3. A works next and the rest is finished on the following day(s): total 12 6/7 days.

6. Example 6उदाहरण 6 · Men, days, hours and work (chain rule) · Mediumमध्यम

   24 workers, working 10 hours a day, finish 2 km of building in 20 days. How many days will 16 workers take to finish 2 km of building, working 6 hours a day?

   1. 13.33 days
   2. 51 days
   3. 50 days
   4. 30 days
   Answer:उत्तर: 50 days

   1. M₁D₁H₁/W₁ = 24 × 20 × 10 / 2 = 2,400 worker-hours per unit.
   2. D₂ = 24 × 20 × 10 × 2 / (16 × 6 × 2).
   3. D₂ = 9,600 / 192 = 50 days.

7. Example 7उदाहरण 7 · Time and work: two people together · Hardकठिन

   Rohan can complete a piece of work in 10 days and Diya in 10 days. They work together for 2 days, then Rohan leaves. In how many more days will Diya finish the remaining work?

   1. 5 days
   2. 6 days
   3. 7 days
   4. 8 days
   Answer:उत्तर: 6 days

   1. Work = 10 units; Rohan = 1/day, Diya = 1/day.
   2. Together for 2 day(s): 4 units. Left: 6 units.
   3. Diya needs 6 ÷ 1 = 6 days.

8. Example 8उदाहरण 8 · Two people working on alternate days · Hardकठिन

   A can do a piece of work in 12 days and B in 13 days. They work on alternate days, B starting. In how many days is the work finished?

   1. 12 12/25 days
   2. 6 6/25 days
   3. 12 6/13 days
   4. 12 1/2 days
   Answer:उत्तर: 12 1/2 days

   1. Total work = 156 units; A = 13/day, B = 12/day; a two-day cycle = 25 units.
   2. 6 full cycles (12 days) do 150 units, leaving 6.
   3. B works next and the rest is finished on the following day(s): total 12 1/2 days.

Common mistakesआम गलतियाँ

• Adding the days instead of the rates.
• Forgetting that one person leaves partway through the job.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न