Question

A person saves every year $ 20\% $ of his income. If his income increases every year by $ 10\% $ , then his savings increase every year by
A. $ 10\% $
B. $ 5\% $
C. $ 2\% $
D. $ 1\% $

Answer 1

Hint: These types of problems are proceeded using formulas of percentage. We know that when any quantity increases by $ x\% $ then the quantity will become $ \left( {1 + \dfrac{x}{{100}}} \right) $ times. We just multiply the percentage number by the previous quantity.

Complete step-by-step answer:
Let us consider that income is $ 100 $ .
The person save $ 20\% $ income then his savings will be
Savings $ = $ $ 20\% $ of $ 100 $
 $ = 20 $
When income is increased by $ 10\% $ then his new income will be $ 110 $
Further his savings can be given as
Savings\[ = 20\% \]of $ 110 $
 $ = 0.2 \times 110 = 22 $
Percentage increase in savings $ = \dfrac{{{\text{final value - initial value}}}}{{{\text{initial value}}}} \times 100\% $
Put the values in above formula
Percentage increase in savings $ = \dfrac{{22 - 20}}{{20}} \times 100 $
 $ = \dfrac{2}{{20}} \times 100 = 10\% $
Hence the percentage increase in savings is $ 10\% $

So, the correct answer is “Option A”.

Note: We should know the formula of calculating percentage when initial value and final value are given. Place the values in the formula very carefully and see which values are increased, accordingly write the value.