You’re given three statements (I, II, and III). Based

Solution

ATQ, Statement I: Time taken by Pipe 'A', 'B' and 'C' together to fill the tank = (t - 7) hours So, efficiency of Pipe 'A', 'B' and 'C' together = {1/(t - 7) } units/hour No information about individual efficiency of pipe 'C' alone. So, data in statement I alone is not sufficient to answer the question. Statement II: Let the efficiencies be pipe 'A' and 'B' be '3y' units/hour and '2y' units/hour respectively. Total capacity of the tank = 3y × (t + 2) units No information about the efficiency of pipe 'C' alone. So, data in statement II alone is not sufficient to answer the question. Statement III: Time taken by Pipe 'A' and 'C' together to fill the tank = (t - 1) hours Efficiency of Pipe 'A' and 'C' = {1/(t - 1) } units/hour But we cannot find the efficiency of pipe 'C' alone So, data in statement III alone is sufficient to answer the question. Combining statements, I and II: Efficiency of Pipe 'C' = {1/(t - 7) } - 3y - 2y = {1/(t - 7) } - 5y = {1 - 5y × (t - 7) } ÷ (t - 7) But we cannot proceed further to obtain the efficiency of pipe 'C' So, data in statement I and II together is not sufficient to answer the question. Combining statements II and III: Let the efficiency of pipe 'C' be 'z' units/hour Combined efficiency of pipe 'B' and 'C' = (2y + z) units per hours Combined efficiency of pipe 'A' and 'C' = (3y + z) units per hours ATQ; 2y + z = (3/4) × (3y + z) 8y + 4z = 9y + 3z z = y So, total work = (3y + z) (t - 1) = 4y(t - 1) units So, 3y(t + 2) = 4y(t - 1) 3t + 6 = 4t - 4 't' = 10 So, time taken by pipe 'C' alone to fill the tank = 4y(10 - 1) ÷ y = 4 × 9 = 36 hours So, data in statement II and III together is sufficient to answer the question. Combining I and III, we get, Combined efficiency of Pipe 'A' and 'C' = {1/(t - 1) } units/hour Combined efficiency of Pipe 'A', 'B' and 'C' = {1/(t - 7) } units/hour We cannot proceed further to find the efficiency of pipe 'C' So, data in statement I and III together is NOT sufficient to answer the question.