Aptitude - Average - Discussion

9. 

A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?

[A]. Rs. 7.98
[B]. Rs. 8
[C]. Rs. 8.50
[D]. Rs. 9

Answer: Option A

Explanation:

Total quantity of petrol
consumed in 3 years
= 4000 + 4000 + 4000  litres
7.50 8 8.50
= 4000 2 + 1 + 2  litres
15 8 17
= 76700  litres
51

Total amount spent = Rs. (3 x 4000) = Rs. 12000.

Average cost = Rs. 12000 x 51 = Rs. 6120   = Rs. 7.98
76700 767


Kiran said: (Jun 9, 2010)  
How to simplify calculation

Dev said: (Nov 23, 2010)  
Explain answers in short cut as much as possible.

Jeevankumar said: (Dec 8, 2010)  
Explain answer in simple logic.

Sriharsha said: (Jan 7, 2011)  
Can any 1 xplain it clearly wit simpl logic.

Muralidhar Reddy said: (Jan 30, 2011)  
Here how average cost calculated any explain me ?

Prince said: (Feb 2, 2011)  
It is not clear very much......

Shivapriya said: (Feb 4, 2011)  
Can anyone explain clearly ?

M.V.Krishna said: (Mar 18, 2011)  
c.p of lit petrol in 1st yr = Rs.7.50
amt spend on petrol = Rs.4000
petrol quantity in 1st yr = (4000/7.50) = 533.33

c.p of lit petrol in 2nd yr = Rs.8.00
amt spend on petrol = Rs.4000
petrol quantity in 2nd yr = (4000/8.00) = 500.00

c.p of lit petrol in 3rd yr = Rs.8.50
amt spend on petrol = Rs.4000
petrol quantity in 3rd yr = (4000/8.50) = 470.58

total quantity of petrol used in 3yrs = 1503.91
total amount spent on petrol = 3*4000 = 12000

so, avg cost of liter petrol = (12000/1503.91)

=7.9

Iswarya said: (Apr 1, 2011)  
Hey thank you krishna that was usful.

Jasmine said: (May 17, 2011)  
Tanks krish. !

Bhupesh said: (Jul 3, 2011)  
I cant understand last calculation that why the reciprocal of the cosumed quatity of the petrol is taken?

Ravi said: (Sep 20, 2011)  
Thanks krishna.

Karuna said: (Oct 18, 2011)  
Other than this any other simple calculation is there ?

Saikumar said: (Nov 21, 2011)  
Thanks krish.

Longanathan said: (Jan 1, 2012)  
Thanks Krish, that was simple and sound.

Nitin said: (Mar 1, 2012)  
Thnks krishna your result is so easy.

Ganapathy said: (Jun 15, 2012)  
What about this.

1yr 7. 50 * 4000 = 30000.
2yr 8. 00 * 4000 = 32000.
3yr 8. 50 * 4000 = 34000.

Total = 96000.
Total amount spend for 3yrs = 4000*3 = 12000.
Avg amt spent for 3 years = 96000/12000 = 8Rs.

Ash said: (Aug 17, 2012)  
Thanks krishna...

Sathish said: (Sep 22, 2012)  
Explain answers in short cut as much as possible.

Gaurav Dudeja said: (Jan 1, 2013)  
What is its short trick?

Akash said: (Apr 2, 2013)  
Look the in the option two closet answer can be 8 or 7.98.

So either can be true but 8 is not possible because of it is not linear so answer will be 7.98.

Sri said: (Aug 6, 2013)  
Can't understand last calculation that why the reciprocal of the consumed quantity of the petrol is taken?

Prakash said: (Aug 9, 2013)  
From start of the calculation onwards we are taken only the reciprocal of the consumed quantity of petrol (i.e).

4000/7.5 = 533.33.

4000/8.00 = 500.

4000/8.5 = 470.58.

Total consumed petrol = 1503.91.

Finally to find avg litre of Petrol = Total amt spend for petrol/total consumed petrol. This is what krishna said in 2011.

Chilo said: (Sep 28, 2013)  
Why not choosing 8 as answer? Please explain.

Rabindra Gouda said: (Nov 15, 2013)  
Most simply answer:

Total amount of rupees/total amount of petrol in litre
3yrs total spent petrol in rupees = 3*4000 = 12000 ........(i).

Total amount of petrol spent in 3year = (4000/7.50)+(4000/8)+(4000/8.50)..........(ii).

Equation (i)divided by equation(ii) we get avg rupees spent per petrol
12000/533.3+500+470.5 = 12000/1503.8 = 7.98(answer).

Lalli said: (Dec 23, 2013)  
Why the 5/18 is divided often, and it can be explained briefly.

Prini said: (Aug 6, 2014)  
Here the question is cost per litre.

So ans = (total cost for 3 years)/(total litres consumed)
= (4000*3)/total petrol litres consumed.

this is the logic.

Smiley said: (Aug 29, 2014)  
How it comes 2/15 + 1/8 + 2/17?

Smiley said: (Aug 29, 2014)  
Can anyone explain this 2/15+1/8+2/17 how it is?

Chippey said: (Sep 25, 2014)  
After taking 4000 as common it is left with.
4000[1/7.50 + 1/8 + 1/8.50].

1/7.50 can be written as 100/750 which is equal to 2/15.
Similarly 1/8.50 can be written as 100/850 which is equal to 2/17.

Ramsreeram said: (Nov 24, 2014)  
Its simple because answer must be close to 7.98 or 8 here averages so it must be ratio form so 7.98.

Nitesh Bhati said: (Mar 17, 2015)  
1st year 4000/7.5 = 533.3.

2nd year 4000/8 = 500.

3rd year 4000/8.50 = 470.5.

= 533.3+500+470.5 = 1503.8.

= 1503.8*7.98 = 4000*3.

= 12000 = 12000.

LHS = RHS.

Jobin said: (Apr 19, 2015)  
Normally average will be Rs. 8 if we won't take the factor of Rs. 4000 per year. When we consider the amount per year, number of liter consumed in the 1st year will be more than second and third.

So approximately the average will be less than 8 and greater than 7.5. And more nearer to 8. So the answer is 7.98.

Gunwanti said: (Jun 25, 2015)  
Can any one explain 76700/51?

Abhishek said: (Aug 10, 2015)  
Where 51 came from?

Gameruler said: (Aug 30, 2015)  
How can we calculate this without using the calculator?

Jeevan J said: (Oct 17, 2015)  
At most one minute is the time available for this question. So further simplifications is required.

Subhasmita said: (Dec 16, 2015)  
Please solve this equation 4000(2/15+1/8+2/17) = ?

Mounika said: (Jan 26, 2016)  
Answer: 1503.92.

Henry said: (Feb 16, 2016)  
When you say approximately. Is it wise to say the answer is 7.98 instead of 8.0 which is B?

Santhosh Sandy said: (Mar 7, 2016)  
In the solution how they got 4000(2/15+1/8+2/17) = (76700/51) ?

I'm bit confused :-(.

Ashwini Madne said: (May 24, 2016)  
@Santhosh Sandy.

= 4000/7.50 + 4000/8 + 4000/8.50.
= 4000(1/7.50 + 1/8 + 1/8.50) ...... 1/7.50.

It can be written as 100/750 which is equal to 2/15 same as 1/8.50 can be written as 100/850 which is equal to 2/17.

= 4000(2/15 + 1/8 + 2/17).
= 4000[{(2 * 8) + (15 * 1)/15 * 8} + 2/17].
= 4000[{31/120 + 2/17}].
= 4000[767/2040].
= 76700/51.

Varma said: (Jul 5, 2016)  
Why take 7.50 + 8 + 8.50 / 3 = 8?

Swaroopa said: (Aug 18, 2016)  
Thank you all for the explanation.

Sandeep said: (Sep 15, 2016)  
Only for this question based upon the options.

Think generally for three years amount is same but the purchasing of petrol is different.

The average is approximately 8 rupees. But in the first year we are purchasing the oil with low price then we get more petrol with the same amount than the other years.

By observing this we get something more in the denominator (petrol quantity) so absolutely numerator value decreases very less than the average (rs. 8).

By seeing options we can say 7.9 is the answer.

Akashay said: (Oct 7, 2016)  
Is there any shortcut to solve this problem?

Venkat said: (Oct 13, 2016)  
Please solve this equation 4000(2/15 + 1/8 + 2/17) = ?

Arvind Sahu said: (Dec 7, 2016)  
As we know,

Average = (tatal cost) / (total quantity).

So according to this question, he is spending 4000/- per yr for 3 corresponding yr.
So total cost become:-
Total cost=4000*3=> 12000/-
And to find total quantity we have to find seperatly first and then add them-
1st yr (4000/7.5) = 533.3,
2nd yr (4000/8) = 500,
3rd yr (4000/8.50) = 470.5.

Total quantity = 533.3 + 500 + 470.5 = 1503.8.

Now we can easily divide and find the average like:-
Required Average = 12000/1503.8
= 7.98 answer.

D Trimurtulu said: (Dec 9, 2016)  
I did not understand this way. Any other way to simplify this problem? Please explain me.

Jeevan said: (Mar 21, 2017)  
Nice, thanks for the explanation @Arvind.

Arif Islam said: (Apr 11, 2017)  
Thanks @Krishna.

Harika said: (Apr 18, 2017)  
Nice explanation @Krishna.

Mizanur Rahman said: (Apr 29, 2017)  
Thanks @Krishna.

Pratik said: (Jun 8, 2017)  
Thanks for the given explanations.

Rajeshwar Singh said: (Jun 24, 2017)  
Hi, everyone the best way to solve the equation is we having value 7.50, 8, 8.50.

For those value whose in the decimal format we wl divide by as per req we wl divide 7.50/100 and there is no need for 8 wl do for 8.50/100 nw we calculate like that 4000(1/7.5+1/8+1/8.5).

4000(100/7.5+1/8+100/8.5).

This will get the value.

Swapn said: (Sep 22, 2017)  
It's a difficult calculation done here

Ganesh said: (Sep 25, 2017)  
Thanks @Krishna.

Mani said: (Oct 17, 2017)  
Answer is very simple when cost is equal in all year, the unit of cost should be average.

Mahadeb said: (Oct 26, 2017)  
Thanks for the explanation.

Mass said: (Feb 28, 2018)  
Here, the Question should be what is the average cost he spent per litre of petrol if he spends 4000 each year? Not the average cost of petrol?

Sharja said: (May 28, 2018)  
Yes, right @Mass.

Subai said: (Jul 3, 2018)  
Thanks, really useful.

Lavina said: (Jul 7, 2018)  
Nice one, it's really helpful, thanks @M. V. Krishna.

Aman said: (Aug 10, 2018)  
1st-year cost of petrol=7.50.
2nd-year cost of petrol=8.
3rd-year cost of petrol=8.50.

The spend amounts each year=4000.
1st-year the quantity of petrol used =4000/7.50=533.33,
2nd yr = 4000/8=500,
3rd yr=4000/8.50=503.33,
total amount spend = 4000 * 3/quantity of petrol use.
12000/1536.66 = 7.9.

Shanmukh Adari said: (Aug 26, 2018)  
It was so useful, thanks for the answer @M.V.Krishna.

Satya said: (Oct 20, 2018)  
It is very easy to understand. Thanks for solving @Krishna.

Arjun said: (Feb 5, 2019)  
7.50/3 + 8/3 + 8.50/3

= 2.5+2.66+2.83 = 7.9.

Shivani Sharma said: (Mar 30, 2019)  
Thanks @Krishna.

Dokuparthi Brahmam said: (Apr 4, 2019)  
Thanks @Krishna.

Shubham said: (Jul 1, 2019)  
In this equation,

= 4000(2/15+1/8+2/17),
= 76700/51.

Raya said: (Aug 4, 2019)  
If you do (7.50+8+8.50)รท3 then you just get the avg per litre cost, but not the average of your spending.

In this question, we need to find the per lit avg cost of your spending you spend Rs 4000. Diff ppl have different avg per litre cost. It depends on how many litres you have used so hence we need to find the litre or amt you have consumed each year.

So, in the last step, we divide the total cost of 3 yrs by total amt of 3 years to GET THE PER LITRE COST OF 3 YEARS WHICH IS NOTHING BUT THE AVERAGE OF 3 YEARS.

Md. Sah-Alam said: (Oct 22, 2019)  
Approximate cost should be 8.

Mohamed Alfaan Mirsha said: (Jan 4, 2020)  
I am not getting this, Can anyone explain me in detail?

Krishna said: (Feb 18, 2020)  
See at last everyone is asking why they have taken reciprocal. The answer is that in the question itself they asked what is the average cost per liter. So we have to find the cost of the amount of petrol not petrol at cost.

Karthik said: (May 1, 2020)  
You are correct, Thanks @Krishna.

Sai said: (Jun 5, 2020)  
Thanks @Krishna.

Sunil Yadav said: (Aug 7, 2020)  
Thanks @Krishna.

Sagar said: (Dec 26, 2020)  
Thanks @Krishna.

Mansingh Budha said: (May 26, 2021)  
I do not understand this problem. How can I solve it? please solve it again.

Sneha said: (Jul 23, 2021)  
= 4000( 100/750) + (1/8) + (100/850).
= 4000(2/15+1/8+2/17) cross multiplication,
= 4000(31/120+2/17) Cross mul,
= 4000(767/2040),
= 3068000/2040 decided by 4 on both side,
= 76700/51.

Shivna said: (Jul 25, 2021)  
Thank you @M.V Krishna.

Surya said: (Aug 19, 2021)  
Thanks @Krishna.

Deeksha said: (Sep 1, 2021)  
Why can't we take the average of cost prices given? Please explain.

Monish S L said: (Sep 11, 2021)  
Thanks @Krishna.

Monish S L said: (Sep 11, 2021)  
Thanks @Krishna.

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