A car is traveling at a uniform speed.The driver sees a milestone showing a 2-digit number. After traveling for an hour the driver sees another milestone with the same digits in reverse order.After another hour the driver sees another milestone containing the same two digits. What is the average speed of the driver?
Ans
45 kmph
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how
ReplyDeletesay those two numbers are a and b
ReplyDeleteso 1st and 2nd milstones displays ab and ba
Few things deduced from it is
1. ba > ab
2. As the 3rd milestone can not have only these two numbers as it has to be different than ab or ba, we will have a three digit number for 3rd milestone which will contain both these numbers.
for any a and b, ba-ab cant be >100 so the distance in two hours will be 2*(ba-ab) and will be some 1xx
so one number is 1 and it has to be the a
now if you say the average speed/hr is x
(b*10+a) - (a*10+b) = x
a=1 so
9b-9 = x
9b-x =9
now
fotr 2nd and 3rd milestone (assume the three digits are a,b and k) and
b*10+a+x = a*100 + (either b*10 + k or k*10 +b)
I tried different values for b here and found following valid
16
61
106
diff 45 (speed)
Can you pls tell me how did you get
ReplyDelete(b*10+a) - (a*10+b) = x
I'm sorry if this qn sounds stupid.
reason is that you are in decimal system
ReplyDeleteplease can have the ans in clarity pls
ReplyDeletethis eqn is correct
ReplyDeleteI don't understand why 1 has to 'a'.. It surely can't be b, but it can be the third digit..
ReplyDelete66kmph works or does the last milestone have to be 3? In fact any 11x s.t. 11x < 100 should work?
ReplyDelete@Parijit, there is one flaw in your reasoning:
ReplyDeleteab to ba and ba to 1XX
you are automatically assuming a = 1 instead of considering the scenario 1ab, in which case:
Let the 2 digits be ab and the speed of the car be x kmph.
Since the car is travelling at uniform speed,
distance from ab to ba = x km
Using above logic, ba > ab
also, after another 1 hr, the driver saw the same digits in another milestone, so the new number has to be 1ab.
so, the distance from ba to 1ab = x
Finally, ab to ba = x
ba to 1ab = x;
distance between ab and 1ab = 100km
2x = 100
x=50;
@parijat
ReplyDeletewhen u travel in a car the value appearing on milestone should decrease, but u have assummed just opposite. please explain
ab=a*10 + b
ReplyDeletebecause , for example 41=4*10+1
121=1*100+2*10+1
After moving from ba - ab = x.
ReplyDeleteWhen finding the difference we know that b, of the second milestone, will be a multiple of 10. The same goes for a in the first milestone.
@thomas:
ReplyDeletenumber, 123 can be represented as,
1 * 100 + 2 * 10 + 3 * 1,
hence number with digits a, b can be represented as,
a * 10 + b
and the reverse of the number ab is ba which is,
b *10 + a
hope you understood!
Yeah, from where did u get the number 10 when you say,
ReplyDelete(b*10+a) - (a*10+b) = x
I wonder if it's a part of the question(that might have got missed out) or I am not good enough in observing it in the question. :)
eg :expand 245
ReplyDelete2*100+4*10+5
200
40
5
the distance in two hours will be 2*(ba-ab) and will be some 1xx.....
ReplyDeletei didnt get it.take that two mile stone 16 and 61.then 61-16=45.2*45=90...how it will be 1xx???
the milestones can be
ReplyDelete21
12
23
32
34
43
45
54
56
65
67
76
78
87
89
98
so as the car travels at uniform speed so the average speed will be the uniform speed only.
Now the difference between the first two milestones will be 9kms and the car travels for 1 hour so 9 kms in 1 hour so uniform speed is 9kmph
why can't the first two numbers be 24/42, 25/52, 26/62,....etc. or 35/53,36/63....etc or 46/64 etc. and so on
DeleteParijat has answered it with a very good explanation 1 Yr before.... :)
ReplyDeletebefore start consider milestone showing 90
Deleteafter an hour it shows the reverse ie 09
again after an hour it shows only the same digits ie either 99 or 00
since 99 cant b it is 00
ans avg speed= distance travld in 2hrs/2
= 90/2
= 45
How could this parajit creature ass-ume a=1!! 1ab could also be possible!!
ReplyDeleteAsume that uniform speed is X, A and B are digits. So BA>AB and BA-AB=x .
ReplyDelete@3th millstone he/she saw a 3 digit number. the number should be a number like this: 100+AB(the 100+BA is not acceptable, it's become very large than its speed) 100+AB= 1AB.
So we have following equations :
BA-AB=X
(100+AB)-BA=X
so by solving above equations(sum two equation and find X) we conclude that X=50.
So simple :D.