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Consider following question

A dishonest shopkeeper makes a cheating of 10% at the time of buying the good and 10% at the time of selling the goods. Find his profit %. 

I am solving it by proportion method. Let the cost price be CP. Then 10% cheating at buying mean, he is taking 1100 gm for every 1000gm. So here multiplication factor comes out to be (1100/1000) ie 11/10.

Now at the time of selling he is cheating again by 10% that means he is giving only 900gm instead of 1000gm. So here multiplying factor would be 10/9.

Now be cascading effect the net multiplying factor on CP comes out to be (11/10 * 9/10) ie 11/9.

So he has a profit of 2 out of 9 ie (200/9)%.

But answer in the textbook is 21%. Please look into and let me know where I am wrong.

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Circle C1 has a radius of 3 units. The line segment
PQ is the only diameter of the circle which is
parallel to the X axis. P and Q are points on curves
given by the equations y + ax and y = 2ax
respectively, where a < 1. The value of a is:

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