A garrison of 2000 men has provision of ration for 66 days. At the end of a fortnight, reinforcement arrives and it is found that ration will last only for 20 days more. The strength of the reinforcement is
(a)2000
(b)2200
(c)2600
(d)3200
Answer
Answer (as printed): D
Explanation
Let the strength of the reinforcement be $x$ men. Then, 2000 men had provisions for $(66-14)=52$ days while $(2000+x)$ men consumed it in 20 days. More men, Less days (Indirect Proportion). $\therefore (2000+x):2000::52:20 \Leftrightarrow 20(2000+x) = 2000 \times 52 \Leftrightarrow (2000+x) = \frac{2000 \times 52}{20} = 5200 \Leftrightarrow x = 3200$.
Explanation as extracted from the printed page; notation may be imperfect.