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- Take total work as 1 or LCM.
- Find each one-day work rate.
- Combine rates as required.
Correct Answer: A
Correct Answer: A
Method / Topic: Time and Work
The answer is based on combined work rates.
Short Explanation
Detailed Explanation
Correct Answer: A
Method / Topic: Time and Work
<p>📖
Aman, Gopal, and Vikram are working on a school renovation task. Each person has a different speed: Aman needs 15 days, Gopal needs 20 days, and Vikram needs 30 days if working alone. The team leader wants to know the time when all three work together. 🔑
For more than two workers, the LCM
is very useful. We assume total work as the LCM of their individual days, convert each worker's work into units per day, and then divide total work by combined daily work. 📝
Aman's time = 15 days Gopal's time = 20 days Vikram's time = 30 days Required value = time together 📐
/
Total work = LCM of given days Total daily work = sum of individual daily work Time = total work / total daily work 🔢
Step 1: Total work = LCM(15, 20, 30) = 60 units Step 2: Aman's daily work = 60/15 = 4 units/day Step 3: Gopal's daily work = 60/20 = 3 units/day Step 4: Vikram's daily work = 60/30 = 2 units/day Step 5: Combined daily work = 4 + 3 + 2 = 9 units/day Step 6: Time = 60/9 = 6.67 days ✅
Therefore, all three will complete the work in 6.67 days. Correct option: A 🏦
This means three people together finish much faster because their daily work adds up.</p>
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Learn + Solve: Shortcut, Trap & Fast Route Click to view shortcut, steps, and common mistake
Shortcut used, common trap, and the fastest solving route
- Take total work as 1 or LCM.
- Find each one-day work rate.
- Combine rates as required.
Aman, Gopal, and Vikram can complete a work in 15, 20, and 30 days respectively. In how many days will they finish it together?
Explanation
Correct Answer: A
Method / Topic: Time and Work
The answer is based on combined work rates.
Short Explanation
Detailed Explanation
Correct Answer: A
Method / Topic: Time and Work
<p>📖
Aman, Gopal, and Vikram are working on a school renovation task. Each person has a different speed: Aman needs 15 days, Gopal needs 20 days, and Vikram needs 30 days if working alone. The team leader wants to know the time when all three work together. 🔑
For more than two workers, the LCM
is very useful. We assume total work as the LCM of their individual days, convert each worker's work into units per day, and then divide total work by combined daily work. 📝
Aman's time = 15 days Gopal's time = 20 days Vikram's time = 30 days Required value = time together 📐
/
Total work = LCM of given days Total daily work = sum of individual daily work Time = total work / total daily work 🔢
Step 1: Total work = LCM(15, 20, 30) = 60 units Step 2: Aman's daily work = 60/15 = 4 units/day Step 3: Gopal's daily work = 60/20 = 3 units/day Step 4: Vikram's daily work = 60/30 = 2 units/day Step 5: Combined daily work = 4 + 3 + 2 = 9 units/day Step 6: Time = 60/9 = 6.67 days ✅
Therefore, all three will complete the work in 6.67 days. Correct option: A 🏦
This means three people together finish much faster because their daily work adds up.</p>
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