ans is 18

Let the actual speed be $s$ km/hr and the distance be $d$ km.

Time = Distance / Speed

Case	Speed	Time Lost
1	$s - 6$ km/hr	20 minutes
2	$s - 2$ km/hr	5 minutes

Case 1 Equation

20 minutes = $\dfrac{20}{60} = \dfrac{1}{3}$ hour

$\frac{d}{s-6} - \frac{d}{s} = \frac{1}{3}$

$\frac{6d}{s(s-6)} = \frac{1}{3}$

$d = \frac{s(s-6)}{18} \quad \text{...(1)}$

Case 2 Equation

5 minutes = $\dfrac{5}{60} = \dfrac{1}{12}$ hour

$\frac{d}{s-2} - \frac{d}{s} = \frac{1}{12}$

$\frac{2d}{s(s-2)} = \frac{1}{12}$

$d = \frac{s(s-2)}{24} \quad \text{...(2)}$

Equating (1) and (2):

$\frac{s(s-6)}{18} = \frac{s(s-2)}{24}$

$\frac{s-6}{18} = \frac{s-2}{24}$

$24(s-6) = 18(s-2)$

$24s - 144 = 18s - 36$

$6s = 108$

$s = 18$

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