Three workers P. Q. R can do a certain job at their own rate separately. If X represents the ratio of the work-speed of P and R, and Y represents the ratio of the work-speed of Q and R. such that \(X < Y\) and \(Y < 1\), who is the fastest worker of the three?

Explanation: Let \(S_P\), \(S_Q\), \(S_R\) be the work-speeds of P, Q, and R. Given: \(X = S_P/S_R\), \(Y = S_Q/S_R\). Conditions: \(X < Y\) and \(Y < 1\). Since \(Y < 1\) and \(Y = S_Q/S_R\), and speed must be positive, it means \(S_Q < S_R\). So, R is faster than Q. Since \(X < Y\) and both have the same denominator \(S_R\), it means \(S_P < S_Q\). Combining the inequalities: \(S_P < S_Q < S_R\). Therefore, **R** is the fastest worker.