A can lay railway track between two specified stations in 16 days, while B can complete the same task in 12 days. When C assists…

Question

A can lay railway track between two specified stations in 16 days, while B can complete the same task in 12 days. When C assists them, they manage to finish the job in just 4 days. How long would it take for C to complete the job on their own?

1. A. \(812\) days
2. B. \(912\) days
3. C. \(935\) days (Correct answer)
4. D. 10 days

Correct Answer

Option C — \(935\) days

Detailed Solution & Explanation

The correct answer is 9⅗ days.

Key Points

• Express each rate as work per day, using an LCM of 48 units for the whole job:
  • A: 48 ÷ 16 = 3 units/day
  • B: 48 ÷ 12 = 4 units/day
  • All three together: 48 ÷ 4 = 12 units/day
• C's rate = 12 − 3 − 4 = 5 units/day.
• C alone takes 48 ÷ 5 = 9.6 = 9⅗ days.

Additional Information

• Taking the LCM of the given times as the total work converts fractions into whole units and is faster and safer than working with 1/16 and 1/12 directly.
• The same method in fractions: 1/16 + 1/12 + 1/C = 1/4, giving 1/C = 1/4 − 7/48 = 5/48.
• The general principle is that rates add while times do not — the commonest error in this topic is averaging the days instead.

प्रश्न (हिन्दी में)

A दो निर्दिष्ट स्टेशनों के बीच रेलवे ट्रैक 16 दिनों में बिछा सकता है, जबकि B उसी कार्य को 12 दिनों में पूरा कर सकता है। जब C उनकी सहायता करता है, तो वे केवल 4 दिनों में काम पूरा कर लेते हैं। C को अकेले काम पूरा करने में कितना समय लगेगा?

1. A. \(812\) दिन
2. B. \(912\) दिन
3. C. \(935\) दिन
4. D. 10 दिन