A person saves \(x\) % of her income.  If her income increases by 26% and the expenditure increases by 20%, then her savings increase by 50%.  What is the value of \(x\) ?

20

Let Income = 100

Savings = Rs. \(x\) 

Expenditure = 100 - \(x\) 

ATQ,

Income increased = 100 × 26% = 26

Expenditure Increased = (100 - \(x\) ) × 20%

Saving Increased = \(x\) × 50%

Now,

Income = Expenditure + Savings

26 = {(100 - \(x\) ) × 20%} + {\(x\) × 50%}

26 = 20 - {\(x\) × 50% - \(x\) × 20%}

26 - 20 = \(x\) × 30%

6 = \(x\) × 30%

\(x\) = 20