Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
A took 15 seconds to cross a rectanglar field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68 m/min. The area of the field is
(a)$30 \mathrm{m}^{2}$
(b)$40 \mathrm{m}^{2}$
(c)$50 \mathrm{m}^{2}$
(d)$60 \mathrm{m}^{2}$
Answer
Answer (as printed): D
Explanation
Length of diagonal $=\left(52 \times \frac{15}{60}\right) \mathrm{m}=13 \mathrm{m}$. Sum of length and breadth $=\left(68 \times \frac{15}{60}\right) \mathrm{m}=17 \mathrm{m}$. $$\therefore \sqrt{l^{2}+b^{2}}=13 \text { or } l^{2}+b^{2}=169 \text { and } l+b=17 .$$ Area $=l b=\frac{1}{2}(2 l b)$ $$\begin{aligned} & =\frac{1}{2}\left[(l+b)^{2}-\left(l^{2}+b^{2}\right)\right]=\frac{1}{2}\left[(17)^{2}-169\right] \\ & =\frac{1}{2}(289-169)=60 \mathrm{m}^{2} . \end{aligned}$$