Question: Two train start at the same time from Hyderabad and Delhi
and proceed towards each other at the rate of 80 km and 95 km per hour
respectively. When they meet it was found that one train has travelled 180 km
more than the other. Find the distance between Delhi and Hyderabad. [हैदराबाद
एवं दिल्ली से दो ट्रेनें क्रमशः 80 किमी/घंटे तथा 95 किमी/घंटे की दर से एक दूसरे
की ओर आ रही हैं. जब वे मिलती हैं, तो एक ट्रेन दूसरी ट्रेन से 180 किमी ज्यादा चल
चुकी होती है. बताइए कि दिल्ली से हैदराबाद की दुरी क्या है?] Ans. (d) 2100 km
(a) 2110 km (b) 2000 km.
(c)2200 km (d) 2100 km (e) None of
these
Detailed
explanation:
First Method : Since both the train take the same time to meet. So,
(x + 180)/95 is equal to x/80
Solving it, we get x = 960 km. Distance described by
the trains from Delhi and from Hyderabad are respectively 960 km and (960 + 180) km. that is, 960 km and 1040
km. Therefore, total distance = 2100 km Ans. [x is the distance described by
the train coming from Hyderabad, when they meet.]
Second Method : Since in the same time, one train describes 180
km more than the other,
so 95t – 80t = 180 so, t = 12 h Total distance = 175 × 12 = 2100 km Ans. [t
is the time taken by each of the train.]
Third Method : Since both the train take the same time to meet,
so the ratio of the distance described by the train will same as the ratio of
the speed of the trains. That is, in the ratio of 95 : 80, that is, in the
ratio of 19 : 16.
Here, difference is 3, while the sum is 35.
(diff.) 3 ≡ 180 km,
1 ≡ 60 km, Total distance = 35 × 60 km = 2100 km Ans.
Fourth Method Time = Since
the speed of the trains are 80 and 95 km/h and one train describes 180 km more
than the other in the same interval of time, so this 180 km is described by the
trains at the rate of 15 km/h (95-80) in 12 hours (180 km/15 km/h).
The trains describe the distance between Delhi and
Hyderabad at the rate of 175 km/h in 12 hours.
So, total distance = 175 km/h × 12h = 2100 km Ans. The best method [relative speed method]
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