Aptitude - Average - Discussion

13. 

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:

[A]. 250
[B]. 276
[C]. 280
[D]. 285

Answer: Option D

Explanation:

Since the month begins with a Sunday, to there will be five Sundays in the month.

Required average
= 510 x 5 + 240 x 25
30
= 8550
30
= 285


Julie said: (Sep 10, 2010)  
Please explain me this more clearly anyone.

Prasad said: (Nov 9, 2010)  
Hi Julie,

In a 30 days month you will get 5 sundays if the 1st day is sunday.

So 5 sundays x 510 = 2550

Remaining 25 days X 240 days =6000.

So 2550 +6000= 8550/30 = 285.

Uttam said: (Jan 30, 2011)  
30/7= 28days+2 odd days
in 28 days 4 days are sunday.
out of 2 odd days 1 day is sunday.
so number of sundays are 5.
remaining days other than sunday=30-5=25.
so total no of visitors for a month=(510*5)+(240*24)=8550.
so average,
8550/30=285.

Kamesh said: (Apr 14, 2011)  
30 Day's so,
30/7 = 28 + 2 day's so, 4 week's +2 days.
S m t w th f sat
S m t w th f sat
S m t w th f sat
S m t w th f sat
S m
5 sunday's
25 other day's

5*510 = 2550
25*240 = 6000

(6000+2550)/30= 285.

Swapna said: (Jun 18, 2011)  
OMG!!! I bow to all those who understand maths>>>. Its a real treasure and talent.

Gaurav said: (Aug 27, 2011)  
I wish that every month should start from sunday. ;).

Ibrahim said: (Nov 27, 2011)  
This is not true. In 30 days, 1st day being Sunday, there are 5 Sundays, ending at 28th day, but there are 5 Mondays and 5 Tuesdays as well (29th and 30th day respectively).

So in order for the average number of visitors on Monday to be 240, the number of Monday visitors in the whole month must be (240*5) = 1200.

So is it with Tuesday - the average number of Tuesday visitors equals (240*5) = 1200.

Those Monday and Tuesday are 29th and 30th days of the given month respectively.

So the number of other days of the week equals 4.

There are 4 Wensedays, 4 Thursdays, 4 Fridays, and 4 Saturdays.

In order for the average number of visitors of each of these days to be equal to 240, each of these days must have taken (240*4)= 960 visitors per month.

So the whole number of visitors per month:= 2550 (Sundays) + 1200 (Mondays) + 1200 (Tuesdays)+ 960 + 960 + 960 + 960 = 8790.
Not 8550 !!!

So the average that we've been solving for is equal to 293. Not 285 !!!

Donkor From Ghana said: (Dec 10, 2011)  
Let see

510 visitors on Sundays
240 on other days
finding the no. of visitors in a month of 30 days starting with Sunday.
7 days= 1 week

Therefore in a week, we have 510*1 + 240*6=1950 visitors

There are 4 weeks and 2 days in a 30 day month
therefore we get 4 weeks=1950x4=7800 and

2 days beginning with a sunday which means sunday and any other day, gives us 510 + 240=750

Therefore average attendants in a month=(7800+750)/30= 285

Muneer.S said: (Sep 21, 2012)  
If a Month starts from Sunday, there will be 5 Sundays.

So 5 Sundays total Number of visitors= 5*510=2550
Remaining days visitors= 25*240=6000 visitors
Total number of visitors for 30 days= 2550+6000= 8550 visitors
Avg number of visitors per day= 8550/30days =285visitors

Raja said: (Aug 20, 2013)  
@Ibrahim:

You are right in logic but you missed the trick.

A month of 30 days starting with Sunday have only 5 Sunday & 5 Monday but not 5 Tuesday.

Look, if you go through the following, you can understand where you are wrong.

Count of Sunday:

Day 1> Day 8> Day 15> Day 22> Day 29.

Therefore, Day 29 is the last Sunday of that month, so if you proceed further, then Day 30 is your final Monday.

You don't have any further 5th Tuesday in this context.

Now you can table your calculation like what you did earlier without counting the non-existing last Tuesday.

So the whole number of visitors per month:= 2550 (Sundays) + 1200 (Mondays) + 240*4(Tuesday) + 960 + 960 + 960 + 960 = 8550.

That is the right answer you will get !

Phanikiran said: (Oct 26, 2013)  
If month begins with any other day. Then how it will be?

Then 4 Sundays and 26 remaining days for a month right?

So then the count will be 510*4 + 26*240. Is this true?

Teja said: (Nov 26, 2014)  
@Julie.

In a month we have to find how many Sundays. So for that in a week now that we have 6 days except Sunday.

i.e; 30/6 = 5.
5 means total Sundays in a month.
Then total 30 days 30-5 = 25.
25 is remaining days. So simple.

Raj said: (Apr 27, 2015)  
Month started with particular day (Sunday, Monday) the month has five week days.

Eg: It starts Sunday in this month we have 5 Sundays.

Ans,

In this give question we have 5 Sunday.

Avg people on Sunday = 510 and normal days = 240.

Difference of avg people on Sunday and normal day = 510 - 240 = 270.

Then 270*5/30 = 45;

Then we have to add this 45 to 240 it gives 285.

540 - 240 = 270.

270*5/30 = 45.

240 + 45 = 285.

Chandra said: (Jan 19, 2016)  
In this question it is not clear that first day of month is Sunday so how could we assume that there is five Sunday in this month.

Please enlighten me.

Swetha said: (Jun 15, 2016)  
@Chandra.

In the question itself, it is revealed that first day is Sunday, so there will be five Sundays and five Mondays.

So the number of visitors on Sundays =510 * 5.
Number of visitors on Mondays = 240 * 5 * 1.
Number of visitors on remaining four days = 240 * 5 * 4.

So, avg num of visitors per day = 8555/30 = 285 visitors.

Engr.Muhammad Ahmed said: (Jul 11, 2016)  
Well done! All people are doing a good job by giving clear explanation. This is a good thing to understand the solution in different ways.

Srinivasa Reddy said: (Aug 27, 2016)  
Why should we have to think the month start with Sunday?

If it starts with Thursday then we are only 2 Sundays?

Abigya Naidu said: (Sep 15, 2016)  
It is given Sunday in question just work for that.

Suhas said: (Sep 22, 2016)  
Exactly right @Abigya & @Srinivas reddy.

Sheeeba said: (Oct 5, 2017)  
Hey, everyone! what if the month has 31 days? There is a possibility of that as well! right?

Can someone please explain?

Steve said: (Dec 10, 2017)  
The average on sundays exceeds the normal day average by= 510-240 = 270,

There are 5 such sundays, so totally we have to adjust = 270 * 5,
Now, this has to be adjusted into all day s of the month = 30 days,
So we have 270 *5 / 30 = 270 / 6 = 45,
If we add this to the original avg we get the answer = 240 + 45 = 285.

Naina said: (Oct 21, 2018)  
@All. Not all months with 30 days have 5 Sundays.

What if there are 4 Sundays in a month of 30 days, then the answer will be 276.

Shubham J said: (Jan 31, 2019)  
@Naina.

In given question, 30 days are mentioned, but according to you not every month has five Sundays but if you noticed that month has started from Sunday when the month started from Sunday it has five Sunday in that month.

Hope you get cleared with that question.

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