Question

Distance between Kanpur and Jaipur is 90 km. Two men started walking towards each other from Kanpur and Jaipur at the same time. The person who started from Kanpur travelled uniformly with an average speed of 5 km/hr, while the other man travelled with a varying speed as follows: in the rest hours his speed was 3 km/hr, in the second hour it was 3.5 km/hr, in the third hour it was 4 km/hr, and so on. When will they meet each other? a ) 9 hours b ) 15 hours c ) 12 hours d) 10 hours e)None of these

Answer 1

Answer:

b is the right answer because it can divide by 12

Answer 2

Answer:

The correct answer to this question is  (a) 9 hours

Step-by-step explanation:

Given that,

The distance between Kanpur and Jaipur is = 90 km

Speed of men started from Kanpur = 5 km/hr

speed of men started from Jaipur in the first hour = 3 km/hr

speed of men started from Jaipur in the second hour = 3.5 km/hr

speed of men started from Jaipur in the third hour = 4 km/hr

and so on........

∴ Distance covered by two men in the rest hours = 5 + 3 = 8 km/hr

Distance covered by two men in the second hour = 5 + 3.5 = 8.5 km/hr

Distance covered by two men in the third hour = 5 + 4 = 9 km/hr

and so on....

we can find a pattern in distances covered and the total distance is calculated as

Total distance = 8 + 8.5 + 9 + 9.5 + 10 + ....................... up to n ,

where n is the distance covered by two men at nth hour

we have, the sum of finite n terms in arithmetic series as

Sn = ( n/2 ) * [2a + (n - 1) *d]

90 = ( n/2 ) * [2 * (8) + (n - 1) * (0.5)]

90 = ( n/2 ) * [16 + (n - 1) * (0.5)]

180 = n * [ 16 + 0.5*n - 0.5]

180 = 16*n + (1/2)*n² - (1/2)*n

360 = 32*n + n² - n

360 = n² + 31*n

n² + 31*n -360 = 0

n² + 40*n - 9*n - 360 =0

n(n + 40) - 9(n+40) = 0

(n + 40) * (n - 9) = 0

n = 9 , -40

but time cannot be a negative quantity, so -40 is neglected

Hence, the time taken by two men to meet each other is = 9 hours

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