1. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Find the time required by the first pipe to fill the tank ? A) 10 hours B) 15 hours C) 17 hours D) 18 hours Ans. B Suppose, first pipe alone takes x hours to fill the tank . Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank. As per question, we get 1x+1x-5=1x-9=>x-5+xx(x-5)=1x-9=>(2x-5)(x-9)=x(x-5)=>x2-18x+45=01x+1x-5=1x-9=>x-5+xx(x-5)=1x-9=>(2x-5)(x-9)=x(x-5)=>x2-18x+45=01x+1x-5=1x-9=>x-5+xx(x-5)=1x-9=>(2x-5)(x-9)=x(x-5)=>x2-18x+45=0 After solving this equation, we get (x-15)(x+3) = 0, As value can not be negative, so x = 15 2. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in A) 144 mins B) 140 mins C) 136 mins D) 132 minw Ans. A Let the slower pipe alone fill the tank in x minutes then faster will fill in x/3 minutes. Part filled by slower pipe in 1 minute = 1/x Part filled by faster pipe in 1 minute = 3/x Part filled by both in 1 minute = 1x+3x=136=>4x=136x=36*4=144mins1x+3x=136=>4x=136x=36*4=144mins1x+3x=136=>4x=136x=36*4=144mins 3. 12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is A) 9 litres? B) 15 bukets C) 17 bukets D) 18 bukets Ans. C Capacity of the tank = (12*13.5) litres = 162 litres Capacity of each bucket = 9 litres. So we can get answer by dividing total capacity of tank by total capacity of bucket. Number of buckets needed = (162/9) = 18 buckets 4. A tank can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tank from empty state if B is used for the first half time and then A and B fill it together for the other half. A) 15 mins B) 20 mins C) 25 mins D) 30 mins Ans. D Let the total time be x mins. Part filled in first half means in x/2 = 1/40 Part filled in second half means in x/2 = 160+140=124 Total = x2*140+x2*124=1=>x2(140+124)=1=>x2*115=1=>x=30mins160+140=124 Total = x2*140+x2*124=1=>x2(140+124)=1=>x2*115=1=>x=30mins160+140=124 Total = x2*140+x2*124=1=>x2(140+124)=1=>x2*115=1=>x=30mins 5. Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full ? A) 3 hours B) 5 hours C) 7 hours D) 10 hours Ans. B (A+B)'s 2 hour's work when opened = 16+14=512(A+B)'s 4 hour's work=512*2=56Remaining work = 1-56=16Now, its A turn in 5 th hour16 work will be done by A in 1 hourTotal time = 4+1=5hours16+14=512(A+B)'s 4 hour's work=512*2=56Remaining work = 1-56=16Now, its A turn in 5 th hour16 work will be done by A in 1 hourTotal time = 4+1=5hours16+14=512(A+B)'s 4 hour's work=512*2=56Remaining work = 1-56=16Now, its A turn in 5 th hour16 work will be done by A in 1 hourTotal time = 4+1=5hours