Q:

# Pumps A, B and C operate at their respective constant rates. Pumps A and B, simultaneously, can fill a certain tank in 6/5 hours. Pump A and C, operating simultaneously, can fill the tank in 3/2 hours; abd pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank?(A) 1/3(B) 1/2(C) 2/3(D) 5/6(E) 1

Accepted Solution

A:
[NOTE: NO OPTION MATCHES THE ANSWER because values provided are wrong but I have solved the qyestion with the given values for your understanding, If B and C will take 1/2 hours then the answer will be 1 that is Option E] Answer:Pumps A and B,A + B = 5/6Pumps A and C,A + C = 3/2Pumps B and C,B + C = 2Now we have to find A + B + C = ?For this we will add all of the above equations from both sides.A+B + A+C +B+C = 5/6 + 3/2 + 2Taking LCM on R.H.S,2A + 2B + 2C = (5+9+12)/62(A+B+C) = 26/62(A+B+C)= 13/3A+B+C = 13/6It will take 13/6 hours if A,B and C are pumped simultaneously.[NOTE: NO OPTION MATCHES THE ANSWER because values provided are wrong but I have solved the qyestion with the given values for your understanding, If B and C will take 1/2 hours then the answer will be 1 that is Option E]Step-by-step explanation: