Multiple choice

A car travels from A to B at a constant speed. If its speed were increased by 20 km/hr it would have been taken half an hour lesser to cover the distance. It would have taken further 10 minutes lesser if the speed was further increased by 10 km/hr. The distance between the two places is? एक कार लगातार गति से A से B तक जाती है। यदि इसकी गति 20 किमी / घंटा बढ़ जाती है तो दूरी तय करने में आधा घंटा कम समय लगता। यदि गति को 10 किमी / घंटा और बढ़ाया जाता तो यह 10 मिनट और कम होता। दो स्थानों के बीच की दूरी क्या है?

  1. 138

  2. 142

  3. 160

  4. 120

  5. 145
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D Correct answer
Explanation

Let original speed = v km/hr, time = t hours, distance = d = vt. Condition 1: speed (v+20), time (t-0.5), so d = (v+20)(t-0.5). Condition 2: speed (v+30), time (t-1), so d = (v+30)(t-1). Equating: vt = (v+20)(t-0.5) = (v+30)(t-1). Solving: vt = vt - 0.5v + 20t - 10 gives 0.5v = 20t - 10. And vt = vt - v + 30t - 30 gives v = 30t - 30. Solving these: t = 4 hours, v = 90 km/hr. Distance d = 90 × 4 = 120 km.

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