Discussion
In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Answer: A
Let Abhay's speed be \( a \) and Sameer's be \( s \).
\[ \frac{30}{a} - \frac{30}{s} = 2 \qquad \text{(i)} \]
\[ \frac{30}{2a} = \frac{30}{s} - 1 \qquad \text{(ii)} \]
From (i), \( \tfrac{30}{s} = \tfrac{30}{a} - 2 \). Substituting into (ii):
\[ \frac{15}{a} = \frac{30}{a} - 2 - 1 \quad\Longrightarrow\quad \frac{15}{a} = 3 \]
\[ a = 5 \text{ kmph} \]
Checking: Abhay takes 6 hours, Sameer 4; at 10 kmph Abhay would take 3 hours - one less than Sameer, as required.
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