The distance from A to B is 60 km. Partha and Narayan start from A at

Question

The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. What is the speed of Partha, in km per hour?

A. 7
B. 6
C. 5
D. 4
E. 3

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A. 7
B. 6
C. 5
D. 4
E. 3

Are You Up For the Challenge: 700 Level Questions

CareerGeek · Answer

Partha takes four hours more than Narayan to reach B
Let the time taken by Partha =  t  & that of Narayan =  t - 4

--> Speed of Partha,  s_p = \frac{60}{t}  & Speed of Narayan,  s_n = \frac{60}{t - 4}

Partha reaches the mid-point of A and B two hours before Narayan reaches B
-->  \frac{60}{s_n} - \frac{30}{s_p} = 2

-->  \frac{2}{s_n} - \frac{1}{s_p} = \frac{1}{15}

-->  \frac{2(t - 4)}{60} - \frac{t}{60} = \frac{1}{15}

-->  2t - 8 - t = 4

-->  t = 12  hours

--> Speed of Partha,  s_p = \frac{60}{t} = \frac{60}{12} = 5  kmph

Option C

preetamsaha · Answer

let time taken by Narayan to reach B = t hour 
So time taken by Partha to reach B = (t+4) hours 
Time taken by Partha to reach mid point of A and B = (t+ 4)/2 
Given t – (t+ 4)/2 = 2 
2t – t – 4 = 4 
t = 8 hours 
Speed of Partha = 60/(t+4) = 60/12 = 5 km/hour 
 Correct option C

exc4libur · Answer

time: 30/p=60/n-2
time: 60/p=60/n+4
equate: 30/p+2=60/p-4
... 30/p=6, 6p=30, p=5

ans (C)

KarishmaB · Answer

Responding to a pm:
Say Partha takes t hrs to reach midpoint of A and B.
Then Narayan takes t+2 hrs to reach B.

Then Parth will take 2t hrs to reach B.
Narayan takes 2t - 4 hrs to reach B.

This means t + 2 = 2t - 4
t = 6 hrs
Speed of Parth = 30km/6 hrs = 5 kmph

fmcgee1 · Answer

This one is really confusing me.

Why can't we make Partha's speed 2t+4 and t-2 and then solve for that? 2t+4 = t-2... but this doesn't work.

Also, one of the answers is giving the equation as 30/t + 2=60/t - 4. This one seems to work, but only if you don't make the denominators "t+2" and "t-4". But what I don't understand here, is if this equation is distance/time = rate, shouldn't the entire time be under the denominator in both of the fractions? It should be 30/(t+2) = 60/(t-4).

I'm also so confused because almost all the answers above, including the ones by experts, are giving different answers for the time (12, 6, and 8)... Yet still coming up with the same answer (C).

sarthak1701 · Answer

How are we assuming by default that half distance will lead to half-time? She could have traveled to the midpoint faster taking less time and then slowed down?

bumpbot · Answer

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The distance from A to B is 60 km. Partha and Narayan start from A at

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