Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

दो पाइप ए और बी एक साथ 4 घंटे में एक कुंड भर सकते हैं। अगर उंहे अलग से खोला गया था, तो बी 6 घंटे से अधिक समय लेता है एक कुंड भरने के लिए ले लिय । ए द्वारा सिस्टर्स को अलग से भरने में कितना समय लगेगा?

Suppose pipe A alone can fill the cistern in xx hours.

Then pipe B alone can fill the cistern in (x+6)(x+6) hours.

Part filled by pipe A in 1 hr =1x=1x

Part filled by pipe B in 1 hr =1x+6=1x+6

Part filled by pipe A and pipe B in 1 hr =1x+1x+6=1x+1x+6

It is given that pipes A and B together can fill the cistern in 4 hours.

i.e., Part filled by pipes A and B in 1 hr =14=14

⇒1x+1x+6=14⇒1x+1x+6=14

From here, it is better to find the value of xx from the choices which will be easier. Or we can solve it as follows.

4(x+6)+4x=x(x+6)4x+24+4x=x2+6xx2−2x−24=0(x−6)(x+4)=0x=6 or −44(x+6)+4x=x(x+6)4x+24+4x=x2+6xx2−2x−24=0(x−6)(x+4)=0x=6 or −4

Since xx cannot be negative, x=6x=6

i.e.,pipe A alone can fill the cistern in 6 hours