The cost of a table and a chair are in the ratio of 5 : 7. If the cost of chair and table is increased by 20% and 10% respectively, then what will be the new ratio?

Let the cost of the table and chair be Rs. 5x and Rs. 7x respectively
$$\eqalign{ & {\text{New cost of chair}} \cr & = 120\% {\text{ of }}7x \cr & = {\text{Rs}}{\text{.}}\left( {\frac{6}{5} \times 7x} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{42x}}{5} \cr & {\text{New cost of table}} \cr & = 110\% {\text{ of }}5x \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{11}}{{10}} \times 5x} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{55x}}{{10}}. \cr & \therefore {\text{New ratio}} \cr & = \frac{{55x}}{{10}}:\frac{{42x}}{5} \cr & = 55:84 \cr} $$