Saturday, 27 June 2015

Time and Distance [समय और दूरी]-02

Question: Without any stoppage a person travels a certain distance at an average speed of 40 km per hour, and with stoppages he covers the same distance at an average speed of 30 km/hr. how many minutes per hour does he stop? [बिना रुके कोई व्यक्ति 40 किमी/घंटे की औसत चाल से एक निश्चित दूरी तय करता है; लेकिन जब रुक रुक कर (ठहराव) के साथ चलता है, तो उसी दूरी को तय करने में उसकी औसत चाल अब 30 किमी/घंटे की हो जाती है. बताएं कि उस व्यक्ति का ठहराव प्रति घंटे कितने मिनट का है?]  [Ans. (c) 15 minutes]

(a) 7 minutes  (b) 7.5 minutes  (c) 15 minutes  (d) 20 minutes  (e) None of these.

Solution:


Detailed Explanation:

First Method: Given that the average speed of the man without stoppages is 40 km/h. That is, the man covers 40 km in one hour. Since the average speed of the man becomes 30 km/h with stoppages, so the man describes 30 km, and rests for the time taken to cover the remaining 10 km. But, remaining 10 should be covered in ¼ of an hour, i. e., 15 minutes; as he covers 40 km in hour. Therefore, stoppages per hour are 15 minutes. Ans.  

Second Method: Since the average speed of the man without stoppages is 40 km/h. It is reduced to 30 km/h due to stoppages; that means, the man goes 30 km and then stop his journey till the hour is completed. But, the time taken to cover 30 km is (30/40) hour or 45 minutes. So, the rest is (60-45) minutes = 15 minutes. Therefore, stoppages per hour are 15 minutes. Ans.

Third Method: In both the journey (without stoppages and with stoppages), the distance covered are the same. So, the time taken will be in the inverse proportion of speeds.

                                                                 Without Stoppage   with Stoppages                                                                     
                                                            S1: S2 =     40 km/h   :  30 km/h Difference
                                                            T1: T2 =      3             :        4      :      1
                                                                                                          4 ≡ 1 hour                     
                                                                                                          1 ≡ ¼ hr = 15 min                          
                                                                                                          = 15 min/hr.  Ans.                  

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