How to solve the problem on percentage? [closed]

Question:

"From 2000 onwards, till 2003 the price of the computers increased every year by 10%. After that due to government subsidy the price of computer decreases every year by 10%. The price of a computer in 2006 will be approx. how much percent less than the price in 2000 if the same pattern if price is continued?"

Doubt:

I really am not able to understand how to solve the problem. I understand that this is successive percentage but beyond that it is difficult for me.

Solution 1:

Let $x$ be the price of computers in 2000. Then

• in 2001 it would be $1.1x$,
• in 2002 it would be $1.1(1.1x)=1.21x$, and
• in 2003 it would be $1.1(1.21)x=1.331 x$.

Afterwards, it goes down $10$% each year, so

• in 2004, it would be $0.9(1.331 x)=1.1979x$,
• in 2005, it would be $0.9(1.1979 x)=1.07811x$,
• in 2006, it would be $0.9(1.07811 x)=0.970299x$.

So, the price of a computer in 2006 is $97.0299$% that of a computer in 2000. In other words, it is $2.9701$% less.