Hii recently ran into this problem and i can't seems to solve it. Can someone enlighten me to the method use to solve it?

P = A1P1 + … + A5P5

Where

A1 + … + A5 = 1

LetAirepresent the weight of good(iwill be a number between 1 and 5)i

Pbe the price level

AndPithe price of goodi

Example

Let the good and weights be given as follow in the table below

Good ---------- Weight (Ai)

Cake -----------0.4

Oil ------------- 0.2

Transport ----- 0.1

Vacations ----- 0.1

Hospital ------- 0.2

Suppose the prices of the various goods change in the following way

Cake +20% (dp1 = 0.2)

Oil +20% (dp2 = 0.2)

Transport +10% (dp3 = 0.1)

Vacations +40% (dp4 = 0.4)

Hospital +10% (dp5 = 0.1)

Given the weights in the table, how much will the Price Level (P) rise? Express your answer in %.

By the way i was wondering if i couldn't get the answer because my interpretation of the meaning of dp1 to dp5

after the price increase was wrong .

I inferred that dp1 after price increase, had an increment of 0.2 to it original value, and so on and so for, for the rest of the dp.

Meaning the new value of dp1 = Original Value of dp1 + 0.2

Did i made a wrong inference? Help on this part much appreciated