Aptitude - Average - Discussion

3. 

A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

[A]. Rs. 4991
[B]. Rs. 5991
[C]. Rs. 6001
[D]. Rs. 6991

Answer: Option A

Explanation:

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

Required sale = Rs. [ (6500 x 6) - 34009 ]

   = Rs. (39000 - 34009)

   = Rs. 4991.

Video Explanation: https://youtu.be/tP4hszReksU


Sriram said: (Aug 5, 2010)  
Please give a short cut for this.

Nowshad said: (Sep 8, 2010)  
Please give a simple solution for this.

Avinash said: (Dec 8, 2010)  
Easy method for this is

Assume a nearest number in given number as average

Suppose 6500 as average
and then write down all as follows
6435+65=6500
6927-427=6500
6855-355=6500
7230-730=6500
6562-62=6500
the last number as y+x=6500
the effective should be zero if 6500 is correct average
+65-427-355-730-62+x=0
x=799
to get effective zero we should have the number is -799
therefore the required number is as follows...
4991(6500-799).
explanation is long but it is less time taken...

Aparna said: (Jan 30, 2011)  
Ya you are exact avinash.

Even all t prblms should be solved by this method.

By considering t nearby value.

Abdus Samadh said: (Feb 4, 2011)  
Mr. Avinash are you sure 6500-799=4991.

Mariya said: (Feb 15, 2011)  
Avg=(6435+6927+6855+7230+6565+x)/6=6500
=(34012+x)=6*6500
x=39000-34012=4988 from this can select nearest ans...

Gautam Sharma said: (Feb 16, 2011)  
At First, Multiply 6500x6=39000 (bcoz avg is asking in Q)

Then, add all the 5 sale i.e 34009,

Deduct 39000 from the total sale i.e.34009, it becomes 4991.

Pankaj said: (Jun 7, 2011)  
6435+6927+6855+7230+6562= 34009
6500*7 =39000
39000-34009 =4991

Bhavana said: (Jul 2, 2011)  
Why do we multiply 6 with 6500.

Naveen Kumar said: (Jul 11, 2011)  
Hi friends...

Here is the shortcut method to find this problem...

given average sale for 6 months is 6500..

but we don't know 6 month reading...let it be x..

now,according to the formula...

(6435+6927+6855+7230+6562+x) /6 = 6500

34009 + x = 39000

x = 4991.

Raj said: (Aug 15, 2011)  
Naveen your explain is easy to understand.

Raj said: (Aug 15, 2011)  
Why should we multiply 6500 with 6 explain me?

Sanjana said: (Aug 19, 2011)  
Naveen you are correct.

Isha said: (Aug 20, 2011)  
Thank you so much naveen its so easy.

Muthulakshmi said: (Aug 27, 2011)  
Naveen your answer is easily understandable. Thank you verymuch.

Roopa said: (Sep 20, 2011)  
Naveen thank you.

Sushmita said: (Feb 5, 2012)  
Thanks naveen.

Sravya said: (Feb 7, 2012)  
Naveen your answer is too good.

Venkat said: (Mar 20, 2012)  
@avinash
i.e,
since 6500 is d average
we write down all as follows
6435+65=6500
6927-427=6500
6855-355=6500
7230-730=6500
6562-62=6500
add all the values (i.e 65,-427,-355,-730,-62) we get -1509 adding it with 6500 we get 4991

Pia said: (Apr 1, 2012)  
HI FOLKS...ITS EASILY CN BE DONE AS:
LET THE SALE OF 6TH MONTH BE X
=>(6435 + 6927 + 6855 + 7230 + 6562 + X)/6=6500
=>(34009+X)/6=6500
=>34009+X=(6500 x 6)
=>X=39000 - 34009
=>X=4991
IE, RS.4991

P .P.Anasuya said: (Jun 7, 2012)  
(6435+6927+6855+7230+6562+y)/6=6500
34009+y=6500*6
Y=39000-34009
Y=4991

Pradeep Kumar said: (Nov 23, 2012)  
Simple way.

(6500*6) = 34009+x.

Then
X = Rs.4991.

Where x= sale in rupees for the sixth month.

Vicky said: (Jul 5, 2013)  
(6535+6927+6855+7230+x)/6 = 6500.

34009+x = 6500*6.

34009+x = 39000.

x = 39000-34009.

x = 4991.

i.e., RS.4991/-.

Franklin said: (Oct 25, 2013)  
Hi friends please use this shortcut (6435+6927+6855+7230+6562+x)/6 = 6500.

34009+x = 32500.

x = 4991.

Gana said: (Nov 5, 2013)  
Hi I got the new way but I don't this right or wrong but answer will be coming.

Total 5 month of purchase : (6435+6927+6855+7230+6562) Total = 34009.
You want 6th month sales so divide in total amount 34009 / 6 = 5668.16.

And less six month average amount 6500 - 5668.16 = 831.94.
Coming total multiple in 6 month 831.94 *6 = 4991.64 /-

Swathy said: (Dec 24, 2013)  
*****digital root concept****

Sale=6+4+3+5=9.

6+9+2+7=6.
6+8+5+5=6.
7+2+3+0=3.
6+5+6+2=1.

s/n = avg;.

avg = 6+5+0+0 = 2.
(9+6+6+3+1+x)/6 = 2.
9+6+6+3+1+x = 2*6.

7+x = 3.
x = 5(7+5 = 1+2 = 3).

4+9+9+1 = 2+3 = 5.
Answer: 4991.

Vignesh Prabhu said: (May 5, 2014)  
Why are we multiplying 6500 with 6 ?

Swetha. said: (May 8, 2014)  
This problem can also be done easily in this way:

Average = sum of observations/no.of observations.

Let the sale in 6th month be x.

We have avg = 6500., no.of months = 6.

Then, according to the above formula,

6500 = 6435+6927+6855+7230+6562+x/6.

=>6500*6 = 34009+x.

=>x = 39000-34009.

=>x = 4991. Hence, we got the sale in 6th month as RS. 4991.

Ankit Yadav said: (Aug 2, 2015)  
Please Rs.6 when come.

Anonymous said: (Aug 29, 2015)  
Friends don't follow any tricks.

You can solve aptitude only if you have know concept so try to know concepts and practice more and more examples.

Then everything will be simple. More the examples you practice faster will be calculation after some time.

Rajkumar said: (Oct 27, 2015)  
(Add all) - (6*6500). Got answer.

Deepika Sharma said: (Jan 19, 2016)  
Let 1 sale of 6th month = x.

= (6435+6927+6855+7230+6562+x)/6 = 6500.

Find the value of x and get answer.

Asif Khan said: (Mar 6, 2016)  
Hi every one @Swetha method is more interesting and easy.

Chintu said: (Sep 2, 2016)  
You gave a nice and easy explanation. Thanks @Naveen Kumar.

Harshithakillari79@Gmail.Com said: (Sep 19, 2016)  
The sum is not 34009, but its 34099.

Karunya said: (Dec 2, 2016)  
Thank you @Naveen.

Ranjeet said: (Feb 5, 2017)  
@Naveen.

Your trick is awesome. Thanks for giving it.

Vishakha said: (Mar 20, 2017)  
Thank you for the explanation.

Shirin said: (Apr 24, 2017)  
Thanks for the given explanation.

Sana said: (Jul 14, 2017)  
@Swathy.

x = 5(7+5 = 1+2 = 3).explain this step.

Dandabata said: (Aug 1, 2017)  
6435+65=6500
6927-427=6500
6855-355=6500
7230-730=6500
6562-62=6500

How this happen?

Hrushi said: (Aug 6, 2017)  
Consecutive months means what?

Priya said: (Aug 16, 2017)  
Consider the sale of 6th month=x.

6435+6927+6855+7230+6562+x/6 = 6500
34009+x/6 =6500

34009+x = 39000.
x = 39000-34009.
x = 4891.

Sazid Khan said: (Dec 22, 2017)  
This problem can also be done easily in this way:

Average = sum of observations/no.of observations.
Let the sale in a 6th month be x.
We have avg = 6500., no.of months = 6.
Then, according to the above formula,
6500 = 6435+6927+6855+7230+6562+x/6.
=>6500*6 = 34009+x.
=>x = 39000-34009.
=>x = 4991. Hence, we got the sale in 6th month as RS. 4991.

Shree said: (Feb 14, 2018)  
Thank you for the detailed explanation. Very useful.

B.Geeth Yeswanth said: (Mar 24, 2018)  
Average=Sum of all observations/no.of observations.

6500=6435+6927+6855+7230+6562+x/6,
6500=34009+x/6,
X=6500*6 -34009,
X=39000-34009,
X=4991.

Binit Jha said: (Mar 29, 2018)  
Solution;

6435+6927+ 6855+ 7230 + 6562+x(let)/6=6500,
34009+x/6=6500,
34009+x=6500*6.
x=39000-34009=4991.

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

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