Subject: General Aptitude · Chapter: Boats and Streams · Exam: · Marks: · Difficulty:
A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in $6 \frac{1}{2}$ hours. The velocity of the current is
(a)1 km/hr
(b)1.5 km/hr
(c)2 km/hr
(d)2.5 km/hr
Answer
Answer (as printed): C
Explanation
Let rate upstream $=x \mathrm{kmph}$ and rate downstream $=y \mathrm{kmph}$. Then, $\frac{24}{x}+\frac{36}{y}=36$ and $$\frac{36}{x}+\frac{24}{y}=\frac{13}{2}$$ Adding (i) and (ii), we get : $$60\left(\frac{1}{x}+\frac{1}{y}\right)=\frac{25}{2} \text { or } \frac{1}{x}+\frac{1}{y}=\frac{5}{24}$$ Subtracting (i) from (ii), we get : $$12\left(\frac{1}{x}-\frac{1}{y}\right)=\frac{1}{2} \text { or } \frac{1}{x}-\frac{1}{y}=\frac{1}{24}$$ Adding (iii) and (iv), we get : $\frac{2}{x}=\frac{6}{24}$ or $x=8$. So, $\frac{1}{8}+\frac{1}{y}=\frac{5}{24} \Leftrightarrow \frac{1}{y}=\left(\frac{5}{24}-\frac{1}{8}\right)=\frac{1}{12} \Leftrightarrow y=12$.$$\therefore \quad \text { Speed upstream }=8 \mathrm{kmph},$$ Speed downstream $=12 \mathrm{kmph}$. Hence, rate of current $=\frac{1}{2}(12-8) \mathrm{kmph}=2 \mathrm{kmph}$.
Explanation as extracted from the printed page; notation may be imperfect.