On the first day of a certain month , the price of oil was

Question

On the first day of a certain month, the price of oil was $80 per barrel. During the month, the price changed on two separate days: during the seventh day of the month it rose by $25, and during another day it fell by $60. If the average day-end price during the 30-day month was $82, what was the average day-end price for the last 10 days of the month?

(A) $45
(B) $51
(C) $57
(D) $63
(E) $69

(A) $45
(B) $51
(C) $57
(D) $63
(E) $69

ankushsambare · Answer

Initial price = $80 per barrel.
On day 7, price rises by $25:
New price = $105.
On another day, price falls by $60:
New price = $45.
Since the average price for 30 days is $82:
Total of all daily closing prices = 30 × 82 = 2460.
Let the $60 drop occur on day n.
Days 1–6: price = 80 for 6 days
Days 7 to (n−1): price = 105
Days n to 30: price = 45
Total price:
6(80) + (n−7)(105) + (31−n)(45) = 2460
480 + 105n − 735 + 1395 − 45n = 2460
60n + 1140 = 2460
60n = 1320
n = 22
So the price dropped on day 22.
Therefore, during the last 10 days (days 21–30):
 
 Day 21: 105 
 Days 22–30: 45 for 9 days  
Average for last 10 days:
(105 + 9×45)/10
= (105 + 405)/10
= 510/10
= 51
 Answer: Option: B ($51 per barrel)

kevincan · Answer

Can anybody think of a shortcut ?

kevincan · Answer

Edited for clarity !

chetan2u · Answer

As  kevincan  too has written, there are shortcuts for almost all questions and you have to just get hang of those.
Here too, weighted average method is the most elegant.

kevincan · Answer

Think in terms of deviations from $80.

If the price had remained $80 for all 30 days, the average would have been $80. Since the actual average was $82, the total deviation above the baseline is

30 × (82 − 80) = 60.

After the increase on day 7, the price is $105, which is +25 relative to the baseline.

After the later decrease of $60, the price becomes $45, which is −35 relative to the baseline.

Let n be the number of days the price was $105.

There are 24 days after day 6, so the remaining 24 − n days were at $45.

Therefore, the total deviation is

25n − 35(24 − n) = 60.

Solving:

25n − 840 + 35n = 60

60n = 900

n = 15.

So the price was $105 for 15 days, namely days 7 through 21. Therefore the drop occurred on day 22.

The last 10 days are days 21–30, with prices:

105, 45, 45, 45, 45, 45, 45, 45, 45, 45.

Their average is

(105 + 9 × 45) / 10 = 510 / 10 = 51.

On the first day of a certain month , the price of oil was

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On the first day of a certain month , the price of oil was

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