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- Take total work as 1 or LCM.
- Find each one-day work rate.
- Combine rates as required.
Correct Answer: D
Correct Answer: D
Method / Topic: Time and Work
The answer is based on combined work rates.
Short Explanation
Detailed Explanation
Correct Answer: D
Method / Topic: Time and Work
<p>📖
Arjun and Karan are completing a repair job. They work together for 15 days, but then Karan has to leave for another duty. Arjun continues alone and must finish the remaining job. 🔑
For leaving-type
Arjun's time = 40 days Karan's time = 60 days Together work time = 15 days Karan leaves Required value = additional days for Arjun 📐
/
Total work = LCM of individual days Remaining work = total work − work done together Additional days = remaining work / finisher's daily work 🔢
Step 1: Total work = LCM(40, 60) = 120 units Step 2: Arjun's daily work = 120/40 = 3 units/day Step 3: Karan's daily work = 120/60 = 2 units/day Step 4: Together daily work = 3 + 2 = 5 units/day Step 5: Work done in 15 days = 5 × 15 = 75 units Step 6: Remaining work = 120 − 75 = 45 units Step 7: Arjun's additional time = 45/3 = 15 days ✅
Therefore, Arjun will take 15 days more. Correct option: D 🏦
This means the remaining worker must finish only the leftover part, not the full project.</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.
Arjun can do a work in 40 days and Karan in 60 days. They work together for 15 days, then Karan leaves. How many more days will Arjun take to finish the remaining work?
Explanation
Correct Answer: D
Method / Topic: Time and Work
The answer is based on combined work rates.
Short Explanation
Detailed Explanation
Correct Answer: D
Method / Topic: Time and Work
<p>📖
Arjun and Karan are completing a repair job. They work together for 15 days, but then Karan has to leave for another duty. Arjun continues alone and must finish the remaining job. 🔑
For leaving-type
Arjun's time = 40 days Karan's time = 60 days Together work time = 15 days Karan leaves Required value = additional days for Arjun 📐
/
Total work = LCM of individual days Remaining work = total work − work done together Additional days = remaining work / finisher's daily work 🔢
Step 1: Total work = LCM(40, 60) = 120 units Step 2: Arjun's daily work = 120/40 = 3 units/day Step 3: Karan's daily work = 120/60 = 2 units/day Step 4: Together daily work = 3 + 2 = 5 units/day Step 5: Work done in 15 days = 5 × 15 = 75 units Step 6: Remaining work = 120 − 75 = 45 units Step 7: Arjun's additional time = 45/3 = 15 days ✅
Therefore, Arjun will take 15 days more. Correct option: D 🏦
This means the remaining worker must finish only the leftover part, not the full project.</p>
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