The weights of two persons A and B are in the ratio of 3 : 5. A's weight increases by 20% and the total weight of A and B together becomes 80kg, with an increase of 25%. By what percent did the weight of B increase ?

Explanation:-

Let the initial total weight of A and B be x kg.
Then, $$\eqalign{ & = 125\% {\text{ of }}x = 80 \cr & \Rightarrow x = 80 \times \frac{{100}}{{125}} = 64{\text{kg}}. \cr & {\text{A's initial weight}} \cr & = \left( {64 \times \frac{3}{8}} \right){\text{kg}} \cr & = 24{\text{kg}}{\text{.}} \cr & {\text{B's initial weight}} \cr & = \left( {64 \times \frac{5}{8}} \right){\text{kg}} \cr & = 40{\text{kg}}. \cr & {\text{A's new weight}} \cr & = 120\% {\text{ of }}24{\text{kg}} \cr & = 28.8{\text{kg}}{\text{.}} \cr & {\text{B's new weight}} \cr & = \left( {80 - 28.8} \right){\text{kg}} \cr & = 51.2{\text{kg}} \cr & {\text{Increase in B's weight}} \cr & = \left( {51.2 - 40} \right){\text{kg}} \cr & = 11.2{\text{kg}}. \cr & \therefore {\text{Increase }}\% \cr & = \left( {\frac{{11.2}}{{40}} \times 100} \right)\% \cr & = 28\% . \cr}$$