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Ankit yadav

· started a discussion

· 1 Months ago

ques wrong (Question: 184411.0 )

options galat hai ... answer should be 5 hours

Question:
Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 km/hr. The second goes at a speed of 8 km/hr in the first hour and increases the speed by  1/2 km/hr in each succeeding hour. After how many hours will the second overtake the first car if both cars go non - stop ? 
Options:
A) 16 hours 
B) 9 hours 
C) 18 hours 
D) 24 hours 
Solution:

Ans: (b)

Suppose the second car overtakes the first car after x hours. Then the two cars travel the same distance in x hours. 

Distance travelled by first car in x hours 

= 10x kms 

Distance travelled by second car in x hours 

= Sum of x terms of A.P with first term 8 and common difference 1/2.

i.e. x/2 [2.8+(x-1) 1/2]

=   \(\cfrac{x(x+31)}{4}\)

ATQ 10x =  \(\cfrac{x(x+31)}{4}\)

x = 9 hours

Knowledge Expert

· commented

· 1 Months ago

@adhu aadhar chaudhary its given that The second goes at a speed of 8 km/hr in the first hour and increases the speed by 1/2 km/hr in each succeeding hour.

adhu aadhar chaudhary

· commented

· 1 Months ago

u r solving it by taking an increment of .5 km/ hr but its given a km/hr. so answer is 5

Knowledge Expert

· commented

· 1 Months ago

9 hour is the only correct answer..........you must solve it properly.........

alternate sol:

let no of hours be t
then distance traveled by first car = 10t
and by second car = 8 + 8.5 + 9 +.....t terms
these two should be equal
10t = t/2 ( 16 + (t-1)0.5)
t = 9 hours
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