Three pipes A, B, and C can fill a tank in 6, 8, and 12 hours respectively. When all three pipes are opened together, they work for 2 hours before pipe C is closed. How much additional time will it take to completely fill the tank after that?

Question / प्रश्न

Three pipes A, B, and C can fill a tank in 6, 8, and 12 hours respectively. When all three pipes are opened together, they work for 2 hours before pipe C is closed. How much additional time will it take to completely fill the tank after that?

तीन पाइप A, B और C क्रमशः 6, 8 और 12 घंटे में एक टंकी भर सकते हैं। तीनों पाइप 2 घंटे तक साथ में चलते हैं, फिर पाइप C बंद कर दिया जाता है। उसके बाद टंकी को पूरा भरने में कितना अतिरिक्त समय लगेगा?

Options / विकल्प

A. $\frac{6}{7}$ hours / $\frac{6}{7}$ घंटे ✅
B. $\frac{2}{6}$ hours / $\frac{2}{6}$ घंटे
C. $\frac{3}{5}$ hours / $\frac{3}{5}$ घंटे
D. $\frac{9}{2}$ hours / $\frac{9}{2}$ घंटे

Answer / उत्तर

✅ $\frac{6}{7}$ hours / $\frac{6}{7}$ घंटे

Solution / समाधान

Total tank capacity / कुल क्षमता

A, B, C efficiencies:

Together:

Work done in 2 hours:

Remaining work:

After C is closed, A and B work together:

Additional time:

✅ Correct Answer / सही उत्तर: $\frac{6}{7}$ hours