Discussion
The distance between two cities in the Himachal Pradesh is 300 km. Two cars A and B start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after two hours of their start is 34 km, then the speed of car A and car B are :
Answer: C
The speeds are 63 km/h and 70 km/h respectively.
The cars move towards each other, so the gap closes at the sum of their speeds. In 2 hours the gap fell from 300 km to 34 km. Let the slower speed be \(x\):
\[ \begin{aligned} 2(x + x + 7) &= 300 - 34 = 266 \\ 2x + 7 &= 133 \\ x &= 63 \end{aligned} \]
So the speeds are 63 km/h and 70 km/h. Check: in 2 hours they cover 126 + 140 = 266 km, leaving 34 km.
The other pairs do not differ by 7 km/h (68 and 70, 63 and 71, 60 and 75), so they fail the given condition at once.
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