Question

दो स्टेशनों x और y के बीच की दूरी 778 किमी है । एक रेलगाड़ी x से y तक की दूरी 84 किमी/घण्टा
की चाल से तथा वापसी की यात्रा 56 किमी/घण्टा की चाल से तय करती है। पूरी यात्रा के लिए,
रेलगाड़ी की औसत चाल किमी/घण्टा में ज्ञात कीजिए ।
Distance between two stations x and y is 778 km. A train covers the journey from x to
y at a speed of 84 kmph and returns to x with a speed of 56 kmph. Find the average
speed of the train (in kmph ) for the whole journey.
(A) 67.2
(B) 70
(C) 68
(D)72 Ans: A​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Distance between two stations x and y is 778 km. A train covers the journey from x to y at a speed of 84 kmph and returns to x with a speed of 56 kmph. Find the average speed of the train (in kmph ) for the whole journey.

(A) 67.2

(B) 70

(C) 68

(D)72

EVALUATION

Here it is given that

Distance between two stations x and y is 778 km.

Now the train covers the journey from x to y at a speed of 84 kmph

So the time taken

$\displaystyle \sf{ = \frac{778}{84} \: \: hour}$

Again the train returns to x with a speed of 56 kmph

So the time taken

$\displaystyle \sf{ = \frac{778}{56} \: \: hour}$

Now the total distance covered

= 778 + 778 km

= 1556 km

Total time taken

$\displaystyle \sf{ = \bigg( \frac{778}{84} + \frac{778}{56} \bigg) \: \: hour}$

Hence the required average speed

$\displaystyle \sf{ = \frac{1556}{\frac{778}{84} + \frac{778}{56}} \: \: kmph}$

$\displaystyle \sf{ = \frac{2 \times 84 \times 56}{84 + 56} \: \: kmph}$

$\displaystyle \sf{ = \frac{9408}{140} \: \: kmph}$

$\displaystyle \sf{ = 67.2 \: \: \: kmph}$

FINAL ANSWER

Hence the correct option is 67.2 kmph

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