a teaser

rajes · Joined: 15 May 2004 Posts: 3

hello

plz help me to solve the problem.

a person is travelling in a car at a constant speed. at an instance the mile stone shows the distance of 2 digits.after 1 hr another milestone reads the
revesed number.after another hr a milestone reads the same two digits seperated by a zero. what is the distance to be travelled.

Rakesh · Joined: 16 Feb 2005 Posts: 1

HI,

You Q says the distance that the first two milestones are having two digit no. however, 3rd milestone shows a three digit no. i.e. the the distance is increasing. (It seems you wanna know the speed, not the distance "to be" Rolling Eyes

travelled)

Since the speed is constant, the difference between the first two nos should be equal to the difference between 2nd and 3rd. Hence the 3rd milestone must be having a figure between 100 and 199 (Got it or not).

But the middle no is 0. So the milestone must be having a no between 101 and 109 (100 cant be possible).

Now take the combination of nos
19, 3rd no= 91 + (91 - 19) = 163
18, 3rd no = 81 + (81- 18 ) = 144
17, 3rd no = 71 + (71- 17) = 125
16, 3rd no = 61 + (61- 16) = 106. Here you are.

Dont start from the 11...You know y. rite Very Happy

Speed = 61 - 16 (or 106 - 61) = 45 MPH.

Hope I answered your Q.

You can try this also...

Any 2-digit no can be represented as = 10x + y
reverse it = 10y+x
diff = 9y - 9x (speed) this cant be zero so y > x
3rd no = (10y + x) + (9y - 9x) = 19y - 8x
But three-digit no can be written as = 100 x + 10 * 0 + y
(since, 2nd digit is 0)

Equate 19y - 8x = 100x + y
Put x=1 (If you are dicey abt this. put x=2, and you will be agree with me, but remember x and y can be whole no only)
y = 6
speed = 9y - 9x = 54 - 9 = 45 MPH

btw, i am a new member of this group, signed up today. planning to appear in CAT 2005. Hope we will work as a team and every1 will get benefit. All the best.

RAW · Joined: 03 May 2005 Posts: 3

Couple of questions why are you using combinations and we are wanting to distance why are you saying that the question is reversed

Rahul Haksar

baskar · Site Admin Joined: 11 Apr 2004 Posts: 41

I think Rakesh gave a very elegant way of solving this question. His approach of looking at combinations is how one should approach questions in CAT.

Here is a equation based approach to solve this question.

Let the value shown in the first mile stone be XY, where X and Y take values between 1 and 9 as the tens place of a 2-digit number cannot be '0'.

Therefore, the value shown in the second milestone is YX.

The value shown in the third milestone is XOY.

The value of the first milestone is therefore, 10X + Y
Second milestone value is 10Y + X and
The value of the third milestone is 100X + Y

We know that the distance traveled between the first and second milestone is the same as the distance traveled between the second and third milestone.

Therefore, 10Y + X - (10X + Y) = 100X + Y - (10Y + X)
Solving this equation, we get 9Y - 9X = 99X - 9Y
or 18Y = 108X or Y = 6X.

Now, if X takes any value other than '1', Y will become a 2-digit number.

Therefore, the first milestone is 16, the second one is 61 and the third one 106.

The distance traveled each hour = 61 -16 = 45.

Hence, speed = 45 mph

Baskar
PGDM IIM C 1994

sweet_indian · Joined: 26 Jan 2006 Posts: 18

Dumbo in CAT · Posted: Sat May 06, 2006 8:46 pm Post subject: the question

So the distance thravelled is 90 km. Thats wats asked.
bye