Days To Exams
Today, there are 4 times as many days to the end of my exams, as there are to the start of my exams.
Tomorrow, there are 5 times as many days to the end of my exams, as there are to the start of my exams.
How many days do my exams last for?
The answer is 12.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
9 solutions
Should the problem be worded better !!
Log in to reply
I have updated the wording to the problem.
You can also submit a clarification request if you feel that the problem is worded badly.
The first exam will be given 4 days from now, and the last exam will be taken 16 days from now. Won't that mean there are 13 days of exams (from the 4th day from now until the 16th day from now)?
Log in to reply
Yes you are right I also input the answer first as 13.. 12 is wrong!
Don't count both the days, beginning and the end because the state of existence of exams don't last for a full day on those days.
Log in to reply
If you insist that the answer is 12, then the question should've been, "how many days are there between my first exam and my last exam", instead of asking how many days did my exam last.
If you take an exam today, and another exam tomorrow, you'd say that you had exams for 2 days. Similarly, if the first exam was given 4 days from now, and the last one 16 days from now, then you should count all the days from the 4th to the 16th, which makes the exams last for 13 days.
Log in to reply
@Mark Ayaay – I do not have exams for 2 whole days. In the first day, there is some time for exams to begin. Exams are not lasting during that time. Similarly, during the second day, exams get over at some point and exams do not last for the remaining time. I have exams for only one full day.
very good
Please identify what day "today" is in relation to the 12 days of exams. Is it the 16th day? From the wording "today" is exists in the time before the exams start but then how is it possible that the time to the beginning is greater than the time to the end?
Let x be the number of days till the beginning of the exams, y the number of days till the end
As of today
4 x = y
and as of tomorrow
5 ( x − 1 ) = y − 1
5 x − 5 = y − 1
substituting 4 x for y
5 x − 4 = 4 x
then x = 4 and y = 1 6
The exams last for y − x = 1 2 days.
the qustn says exactly opposite to what u did!!!
Log in to reply
Actually you have been mistaken, the question has been a bit twisted and it appears like the first equation should have been
4 y = x
but this is wrong, read the question carefully and u would get it.
if i am wrong,please elaborate ur methord
I solved it exactly the way you did... Nice solution!!!
s = length of days to the start of the exam. e = length of days of actual exam. so, s + e = 4s, and (s-1) + e = 5(s-1). solve for e = 12
End/start = 4 therefore End = 4 Start
(End-1)/(Start-1)=5 therefore End = 5 Start -4
5 Start -4 = 4 Start
Start = 4
Exam duration = 4 Start - Start = 3 Start
Exam duration = 12
Ur question is wrong....you have to put yesterday in the place of tomorrow...... So the answer is 30 otherwise we can't find the answer ....fuc* u....
e = 4 s
e − 1 = 5 ( s − 1 )
4 s − 1 = 5 s − 5
s = 4 , e = 1 6 , n = 1 2
Comment: n should actually be 1 2 + 1 = 1 3
Yes it should be 13.. I also input 13 first.. 12 is wrong!
Let x and y be the no of days to the start of exams and no of days to the end of the exams respectively. Thus, 4x=y and 5(x+1)=y+1 Solving for x and y gives: x=-4 ; y=16 Thus total days the exam will last = x+y = 12 days
why did you take 5(x+1) = y+1 ? for tomorrow no of day to the end should decrease rather than increasing.
nice
@Ashok Nimmala I've the same doubt as of you
today---------> x=4y --------->1
tomorrow----> x-1=5(y-1)
x= 5y-5+1
x=5y-4 ----------->2
then
1=2
4y=5y-4
y=4 ------->days to the start of exam
x= 4y= 16 ------>days to the end of exam
then days my exam last for is = 16 -4 = 12
Let:
Da = days before exam
Db = days to last day of exam
Db - Da = days of exam
4Da = Db < equation 1
5(Da - 1) = Db - 1
5Da - 5 = Db - 1
5Da - 4 = Db < equation 2
Substitute value of Db from equation 1
5Da - 4 = 4Da
5Da - 4Da = 4
Da = 4 days
Subtitute in equation 1 to get Db
Db = 4Da
Db = 4(4) = 16 days
days of exam = Db - Da = 16 - 4
days of exam = 12 days
4Da = Db < equation 1: This is incorrect! The problem states that "there are 4 times as many days to the start of my exams, as there are to the end of my exam." Therefore Da = 4Db, isn't it? For eg: In the statement that 32 is 4 times 8, it is incorrect to equate this by 4(32) = 8
Log in to reply
I realize that the wording has been edited but I solved the problem as stated initially. There are 2 situations in which the times to the start is greater than the times to the end: 1. If "today" occurred during the course of the exams and 2. If "today" occurred after the exams. My challenge: Solve the problem as initially stated !
The problem has been edited already. But still that "," should also be omitted to justify "as many as" and not "as many, as" .
when the days to exams last and days to begin were subtracted 3x days were left for exams. now when the next day there were x-1 days to begain and 5x-5 days to end. so there were 4x-4 days for exans. so, 4x-4=3x so, x=4 and 3x=4x-4=12
The difference between the number of days for my exams to begin and the number of days for my exams to end stays constant because as each day passes, both the number of days decreases by 1.
The difference on the first day is 4 x − x = 3 x ,
The difference on the next day is 5 ( x − 1 ) − ( x − 1 ) = 5 x − 5 − x + 1 = 4 x − 4
Since these are equal, 3 x = 4 x − 4 , which gives x = 4 .
The number of days for which my exams lasted is the difference between the number of days for my exams to begin and the number of days for my exams to end. So, my exams lasted for 3 x or 4 x − 4 days ( It doesn't matter which expression you take because both are equal ). Substituting the value of x , we get 1 2 . So, my exams lasted for 12 days.