Aptitude - Average - Discussion

To find the approximate average cost per litre of petrol over the three years, we can calculate the weighted average based on the amounts spent each year.

Let's break down the problem:

Year 1:
Cost per litre = Rs. 7.50
Amount spent = Rs. 4000

Year 2:
Cost per litre = Rs. 8
Amount spent = Rs. 4000

Year 3:
Cost per litre = Rs. 8.50
Amount spent = Rs. 4000.

Total amount spent over three years = 3 * Rs. 4000 = Rs. 12000,

Now, let's calculate the weighted average cost per litre:
Weighted average cost per litre = (Cost per litre in Year 1 * Amount spent in Year 1 + Cost per litre in Year 2 * Amount spent in Year 2 + Cost per litre in Year 3 * Amount spent in Year 3)/Total amount spent.

Weighted average cost per litre = (7.50 * 4000 + 8 * 4000 + 8.50 * 4000)/12000
Weighted average cost per litre = (30000 + 32000 + 34000)/12000
Weighted average cost per litre = 96000/12000,
Weighted average cost per litre = Rs. 8.

So, the approximate average cost per litre of petrol over the three years is Rs. 8.

If you do (7.50+8+8.50)÷3 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.

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.

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

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.

A car owner buys the petrol in 1st year will be = 4000/7.5 = 533.33 litres.
A car owner buys the petrol in 2nd year will be = 4000/8 = 500 litres,
A car owner buys the petrol in 3rd year will be = 4000/8.5 = 470.58 litres,
Total Petrol in 3 year will be = 1503.91 litre

Now the total amount invested in 3 year will be = 4000 * 3 = 12000.
So, the average cost of petrol per litre will be = 12000/1503.91 = 7.98 Rs (approx).

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).

@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.

Expenditure = price * consumption.

For
1st yr consumption = 4000/7.5 = 533.33 ltr.
2nd yr consumption = 4000/8 = 500 ltr.
3rd yr consumption = 4000/8.5 = 470.58 ltr.

Average consumption per yr = sum of all/3 = 501.307 ltrs.

Expenditure = price * consumption.
4000 = price * 501.307.
price = 4000/501.307 = 7.979139505.

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.