CAT 2001 QA Question 19 · Arithmetic - Time, Speed & Distance

Let the speed of Rahul in still water be p and speed of current be q miles per hour.

$\therefore \frac{12}{(p+q)}=\left\{\frac{12}{(p-q)}-6\right\}$ ...(i)

$\therefore \frac{12}{(2p+q)}=\left\{\frac{12}{(2p-q)}-1\right\}$ ...(ii)

12_p − 12_q = 12_p + 12_q − 6(p − q)(p + q)

On solving, we get,

4q = p² − q²                                    … (iii)

24p – 12q = 24p + 12q – (4p² − q²)

On solving we get,

4p² − q² = 24q                                … (iv)

Solving (iii) and (iv), we get,

24q = 9q²

$q=\frac{8}{3}$

Hence, option (d).