Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships, 3 medium ships carry the same amount of water as 2 large ships and 1 small ship. 15 large, 7 medium and 14 small ships, each made 36 journeys and brought a certain quantity of water. In how many journeys would 12 large, 14 medium and 21 small ships bring the same quantity? (M.A.T., 2007) QUANTITATIVE APTITUDE
(a)25
(b)29
(c)32
(d)49
Answer
Answer (as printed): B
Explanation
4 large ships $\equiv 7$ small ships $\Leftrightarrow$ 15 large ships $=\left(\frac{7}{4}\times15\right)$ small ships $=\frac{105}{4}$ small ships. Also, 2 large ships $=\left(\frac{7}{4}\times2\right)$ small ships $=\frac{7}{2}$ small ships. 3 medium ships $\equiv$ 2 large ships + 1 small ship $\equiv\left(\frac{7}{2}+1\right)$ small ships $=\frac{9}{2}$ small ships. $\Leftrightarrow$ 7 medium ships $=\left(\frac{9}{2}\times\frac{1}{3}\times7\right)$ small ships $=\frac{21}{2}$ small ships. $\therefore$ (15 large + 7 medium + 14 small) ships $\equiv\left(\frac{105}{4}+\frac{21}{2}+14\right)$ small ships $=\frac{203}{4}$ small ships. (12 large + 14 medium + 21 small) ships $\equiv\left[\left(\frac{7}{4}\times12\right)+\left(\frac{21}{2}\times2\right)+21\right]$ small ships $=(21+21+21)$ small ships $=63$ small ships. Let the required number of journeys be $x$. More ships, Less journeys (Indirect Proportion). $\therefore 63:\frac{203}{4}::36:x \Leftrightarrow 63x=\frac{203}{4}\times36=1827 \Leftrightarrow x=\frac{1827}{63}=29$.
Explanation as extracted from the printed page; notation may be imperfect.