Question

For covering a distance of P km, a man takes 't' hours. He takes 40 min less if he moves 3 km/h faster. But, if he moves slower by 2 km/h, he takes 40 min more. Then, P is equal to:

• A. 22.5 km
• B. 32.5 km
• C. 42.5 km
• D. None of these

Answer 1

The correct option is D None of these

Let speed be x km/h
Case I $\frac{p}{x}-\frac{p}{x+3}=\frac{40}{60}$
Case II $\frac{p}{x-2}-\frac{p}{x}=\frac{40}{60}$
$\frac{p}{x}-\frac{p}{x+3}=\frac{p}{x-2}-\frac{p}{x}\frac{2p}{x}=p(\frac{1}{x-2}+\frac{1}{x+3})\frac{2}{x}=\frac{2x+1}{x^2+x-6}2x^2+2x-12=2x^2+x$
x = 12 km/h
Therefore, $\frac{P}{12}-\frac{P}{15}=\frac{2}{3},or,\frac{3}{60}=\frac{2}{3}$
Hence, P = 40 km