IBPS PO Prelims practice question
A boat's speed in still water is 15 km/h. It covers 36 km downstream and 24 km upstream, and it is found that the upstream trip takes 36 minutes longer than the downstream trip. Find the speed of the current.
From a IBPS PO Prelims Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (D) 5 km/h
Let current = c. Downstream time = 36/(15+c), upstream time = 24/(15−c). Given 24/(15−c) − 36/(15+c) = 0.6 hour. Multiplying out: 24(15+c) − 36(15−c) = 0.6(225−c²) → 360+24c−540+36c = 135−0.6c² → 60c−180 = 135−0.6c² → 0.6c²+60c−315=0 → c²+100c−525=0. Solving, (c−5)(c+105)=0, so c = 5 km/h (rejecting the negative root).
हिंदी में प्रश्न
एक नाव की स्थिर जल में चाल 15 किमी/घंटा है। यह 36 किमी धारा के अनुकूल और 24 किमी धारा के प्रतिकूल तय करती है, और पाया जाता है कि प्रतिकूल यात्रा में अनुकूल यात्रा से 36 मिनट अधिक समय लगता है। धारा की चाल ज्ञात कीजिए।
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सही उत्तर: (D) 5 किमी/घंटा
मान लीजिए धारा की चाल = c। अनुकूल समय = 36/(15+c), प्रतिकूल समय = 24/(15−c)। दिया है 24/(15−c) − 36/(15+c) = 0.6 घंटा। सरल करने पर: 24(15+c) − 36(15−c) = 0.6(225−c²) → 360+24c−540+36c = 135−0.6c² → 60c−180 = 135−0.6c² → 0.6c²+60c−315=0 → c²+100c−525=0। हल करने पर, (c−5)(c+105)=0, अतः c = 5 किमी/घंटा (ऋणात्मक मूल अस्वीकृत)।
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