UP Police Constable practice question
A train covers the 120 km distance between two stations at a certain uniform speed. On its return journey along the same route, its speed is 20 km/h less than before, and as a result the return journey takes exactly 1 hour longer than the onward journey. Find the average speed of the train for the entire to-and-fro journey.
From a UP Police Constable Quantitative Aptitude practice set · Quantitative Aptitude
Tap an option to check your answer.
Show answer and explanation
Correct answer: (A) 48 km/h
Let the onward speed be s km/h, so the return speed is (s-20) km/h.
120/(s-20) - 120/s = 1
=> 120s - 120(s-20) = s(s-20)
=> 2400 = s2 - 20s
=> s2 - 20s - 2400 = 0 => (s-60)(s+40) = 0 => s = 60 km/h.
Return speed = 40 km/h.
Average speed for the round trip = 2×60×40/(60+40) = 4800/100 = 48 km/h.
120/(s-20) - 120/s = 1
=> 120s - 120(s-20) = s(s-20)
=> 2400 = s2 - 20s
=> s2 - 20s - 2400 = 0 => (s-60)(s+40) = 0 => s = 60 km/h.
Return speed = 40 km/h.
Average speed for the round trip = 2×60×40/(60+40) = 4800/100 = 48 km/h.
हिंदी में प्रश्न
एक ट्रेन दो स्टेशनों के बीच की 120 किमी दूरी किसी स्थिर चाल से तय करती है। उसी मार्ग से वापसी यात्रा में इसकी चाल पहले से 20 किमी/घंटा कम हो जाती है, जिसके परिणामस्वरूप वापसी यात्रा में जाने वाली यात्रा से ठीक 1 घंटा अधिक समय लगता है। पूरी आने-जाने की यात्रा के लिए ट्रेन की औसत चाल ज्ञात कीजिए।
उत्तर जाँचने के लिए किसी विकल्प पर टैप करें।
उत्तर और व्याख्या देखें
सही उत्तर: (A) 48 किमी/घंटा
मान लीजिए जाते समय की चाल s किमी/घंटा है, तो वापसी की चाल (s-20) किमी/घंटा है।
120/(s-20) - 120/s = 1
=> 120s - 120(s-20) = s(s-20)
=> 2400 = s2 - 20s
=> s2 - 20s - 2400 = 0 => (s-60)(s+40) = 0 => s = 60 किमी/घंटा।
वापसी चाल = 40 किमी/घंटा।
पूरी यात्रा के लिए औसत चाल = 2×60×40/(60+40) = 4800/100 = 48 किमी/घंटा।
120/(s-20) - 120/s = 1
=> 120s - 120(s-20) = s(s-20)
=> 2400 = s2 - 20s
=> s2 - 20s - 2400 = 0 => (s-60)(s+40) = 0 => s = 60 किमी/घंटा।
वापसी चाल = 40 किमी/घंटा।
पूरी यात्रा के लिए औसत चाल = 2×60×40/(60+40) = 4800/100 = 48 किमी/घंटा।
More solved Quantitative Aptitude questions
- Batch 1 of a coaching institute has 50 students with an average score of 55 marks, and Batch 2 has 30 students with an average score of 75…
- If 7 notebooks cost ₹630, what is the cost of 16 notebooks?
- A shopkeeper has two articles, A and B, with cost prices ₹600 and ₹900 respectively (total CP = ₹1500). Article A is marked at ₹800 and…
- Find the area of the triangle with vertices A(-4, 8), B(6, -2) and C(-7, -6).
- Ramesh mixes Grade-B tea (cost Rs 60 per kg) with Grade-A tea in the ratio 3:4 (cheaper : dearer). The mixture is sold at Rs 168 per kg…
- The average weight of 10 students in a class is 42 kg. When the weight of the teacher is included, the average becomes 44 kg. Find the…