CAT 2020 Quant Question [Slot 2] with Solution 04

Let the individual times taken by John, Jack and Jim to complete the works be a, b and c respectively.

Given, \(a = 2b \cdots (1)\)

\(\frac{{bc}}{{b + c}} = \frac{1}{3}(a) \cdots (2)\)

\(a - \left( {\frac{{abc}}{{ab + bc + ac}}} \right) = 3 \cdots (3)\)

From (1) and (2), we've \(c = 2b\)

\(\therefore 2b - \left( {\frac{{2b \times b \times 2b}}{{(2b)(b) + b(2b) + (2b)(2b)}}} \right) = 3\)

\( \Rightarrow b = 2\)

\(\therefore c = 4\)