A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:
एक आदमी ने एक निश्चित दूरी को कुछ गति से तय किया। यदि वह 3 किमी/घंटा तेज चलता, तो उसे 40 मिनट कम लगते। यदि वह 2 किमी/घंटा धीमी गति से चलता, तो उसे 40 मिनट अधिक लगते। दूरी (किमी में) है:
Let the speed and time taken by man be respectively x and y.
So the distance = speed*time = xy
I Condition
If he moved 3 kmph faster, he would have taken 40 minutes less.
Now his speed = x+3
Time = y-40/60 = y-⅔ = 3y-2 /3 hr
Distance = speed*time = (x+3)*(3y-2)/3
Distance is same so -
Distance covered with actual speed = distance covered with new speed
xy = (x+3)*(3y-2)/3
3xy = 3xy+9y-2x-6
9y-2x = 6….(1)
II condition -
If he had moved 2 kmph slower, he would have taken 40 minutes more.
Now his speed = x-2
Time = y+40/60 = y+⅔ = 3y+2 /3
Distance = speed*time = (x-2)*3y+2 /3
Distance is same so -
Distance covered with actual speed = distance covered with new speed
xy = (x-2)*3y+2 /3
3xy = 3xy-6y+2x-4
2x-6y = 4….(2)
After solving equation (1) and (2)
y = 10/3
Put the value of y in equation (1)
9y-2x = 6
9*10/3 - 2x = 6
30 -2x = 6
2x = 24
x = 12
Hence the distance = xy = 12*10/3 = 40 km.
So the correct answer is option D.
माना आदमी की गति और समय क्रमशः x और y है।
तब दूरी = गति * समय = xy
I स्थिति
यदि वह 3 किमी/घंटा तेज चलता, तो उसे 40 मिनट कम लगते।
नई चाल = x+3
नया समय = y-40/60 = y-⅔ = 3y-2 /3 घंटा
दूरी = गति*समय = (x+3)*(3y-2)/3
दूरी समान है -
वास्तविक गति से तय की गई दूरी = नई गति से तय की गई दूरी
xy = (x+3)*(3y-2)/3
3xy = 3xy+9y-2x-6
9y-2x = 6….(1)
II स्थिति
यदि वह 2 किमी/घंटा धीमी गति से चलता, तो उसे 40 मिनट अधिक लगते।
अब उसकी चाल = x-2
समय = y+40/60 = y+⅔ = 3y+2 /3
दूरी = गति*समय = (x-2)*3y+2 /3
दूरी समान है -
वास्तविक गति से तय की गई दूरी = नई गति से तय की गई दूरी
xy = (x-2)*3y+2 /3
3xy = 3xy-6y+2x-4
2x-6y = 4….(2)
समीकरण (1) और (2) को हल करने के बाद
y = 10/3
y का मान समीकरण में रखें (1)
9y-2x = 6
9*10/3 - 2x = 6
30 -2x = 6
2x = 24
x = 12
अत: दूरी = xy = 12*10/3 = 40 किमी.
इसलिए सही उत्तर विकल्प D है।
