Question

A train of length L overtakes a cyclist travelling in the same direction in 20 seconds. It travels for 15 minutes from the time it starts overtaking the above cyclist before it starts overtaking a second cyclist coming in from opposite direction in 18 sec. In how many seconds after the train has crossed the second cyclist do the two cyclist meet each other.

Answer 1

options are:
8750
8962
8982
Cannot be determined

I am getting 8082

Answer 2

1) Horrible problem statement. A train cannot "overtake" a cyclist traveling in the opposite direction. "Meets", okay, I'd buy that. "Passes"? Okay.

2) Horrible problem statement. "Train has crossed the second cyclist"? What?? Did the cyclist fail to get out of the way of the train?

Can we decipher?

For the same of argument, the train and the 1st cyclist are going north. The second cyclist is going south. Here are your important landmarks in chronological order...

1) Tran catches Cyclist #1 (Cyclist is in the same spot as the front of the train.)
2) Exactly 20 seconds after Landmark #1, Train passes Cyclist #1 (Cyclist is in the same spot as the back of the train.)
3) Exactly 15 minutes past landmark 1 - This contains all the time to pass cyclist #1), the train meets the southbound Cyclist #2. The front of the train and the cyclist are in the same spot.)
4) Exactly 18 seconds after Landmark #3, the train has passed Cyclist #2 (The back of the train is in the same place as the cyclist.)

Assumptions:
A) Length of the train is constant.
B) Speed of the train is constant.
C) Cyclists have no mass. They are traveling points in space.

A few ideas, using Distance = Rate * Time

Passing Cyclist #1 Train Length = (Train Speed - Cycle #1 Speed) * 20 sec
Passing Cyclist #2 Train Length = (Train Speed + Cycle #2 Speed) * 18 sec

There's a ton of stuff in there. Keeping it organized is the toughest part. Please demonstrate how you arrived at your answer.

Answer 3

I agree with the first objection."Overtaking" is not the right word there. "Meeting and passing" is correct.

I took the speeds as vT,vC1,vC2 of the train, first and second cyclist respectively. L is length of train.

The above 2 eqns you wrote will give:

vC1=vT-L/20 ................1
vC2=L/18-vT .....................2

Look at the figure in the attached file where i have drawn the positions of C1,C2 and train at relevant times. At t=0 ,the train has started overtaking the C1. It travels for 900 sec and meets C2 at a distance of x from initial position.

x'=900*vT ..................3

x'' is the distance C1 has furthur moved in 900 sec.

x''=900*vC1 ...............4

x is the distance between C1 and C2 now

x= 900*(vT-vC1) ...................5

time taken by C1 and C2 to meet = x/(vC1+vC2)
=900*(vT-vC1)/(vC1+vC2)

Substituting the values of vC1 and vC2 from 1 and 2 we will get

time=8100 sec.

This is the time taken by 2 cyclists to meet after the train has met C2. But we are asked the time taken for them to meet after the train has passes C2. So, we have to subtract
18 sec from above which gives: t=8082 sec.

Answer 4

someone also check this question. it also has a little confusing statement :

If a person can buy at 20% less than usual and sell at 10% more than usual, his profit increases by 33% of the usual cost price. Find the initial profit percentage.

Answer 5

@tkhunny

Answer 6

W = Wholesale Price
P = R - W = Profit at Regular Retail
R = W + P = Regular Retail
P/R = 1 - W/R = Original Profit Percentage

I think it means this:

P2/R2 = New Profit Percentage
P2 = R2 - W2
P + 0.33R = 1.1R - 0.80W
P = 0.77R - 0.80W
P/R = 0.77 - 0.80W/R

So, 1 - W/R = 0.77 - 0.80W/R
or, 0.23 = 0.20W/R
and W/R = 0.23/0.20 = 1.15 <== Which makes no sense.

Perhaps it INTENDED to mean this:

P2/R2 = New Profit Percentage
P2 = R2 - W2
1.33P = 1.1R - 0.80W
P = 0.827R - 0.602W
P/R = 0.827 - 0.602W/R

So, 1 - W/R = 0.827 - 0.602W/R
or, 0.173 = 0.398W/R
and W/R = 0.173/0.398 = 0.435 <== Which is plausible.

Answer 7

I think your cyclists aren't moving for part of what you are doing. I get 8262 with some caveats. My current lean is that there is not enough information. I'm willing to be wrong.