What is the cost price of the chair?
I. The chair and the table are sold at profits of 15% and 20% respectively.
II. If the cost price of the chair is increased by 10% and that of the table is increased by 20%, the profit reduces by Rs. 20.

Let the cost price of the Chair be x and that of the table be y.
Using statement 1)
Hence we get the total selling price = 1.15x + 1.2y and profit = 0.15x + 0.2y 
Using this alone we can't find the cost price of the chair.
Using Statement 2)
Total cost price = 1.10 x + 1.2y
Using Statement 1 and 2 together,
We get profit in second case = 0.05x.
Reduction in profit = (0.15x + 0.2y) - 0.05x = 0.1x + 0.2y = 20
Hence we can't deduce the value of x even after using both statements together.