Question : The income of A is 80% of B's income and the expenditure of A is 60% of B's expenditure. If the income of A is equal to 90% of B's expenditure, then by what percentage are the savings of A more than B's savings?

Option 1: 125%

Option 2: 140%

Option 3: 100%

Option 4: 150%

Correct Answer: 140%

Solution : The income of A is 80% of B's income.
The expenditure of A is 60% of B's expenditure.
The income of A is equal to 90% of B's expenditure.
Let the income of B be $100\text{x}$.
So,
Income of A $= (100\text{x} × \frac{80}{100})= 80\text{x}$
For B's expenditure
90% of B's expenditure = A's income
$\therefore$ B's expenditure $= \frac{100}{90} × 80\text{x}= (\frac{100\times8\text{x}}{9})=  \frac{800\text{x}}{9}$
For A's expenditure
A's expenditure = 60% of B's expenditure $= ( \frac{60}{100}\times \frac{800\text{x}}{9})
= \frac{160\text{x}}{3}$
Now,
Savings of A = Income of A – Expenditure of A $= (80x - \frac{160\text{x}}{3})
= \frac{240\text{x} - 160\text{x}}{3}
= \frac{80\text{x}}{3}$
Now,
Savings of B =  Income of B – Expenditure of B $= (100\text{x} – \frac{800\text{x}}{9})
= \frac{900\text{x} - 800\text{x}}{9}
= \frac{100\text{x}}{9}$
Now,
Required percentage increase
= $\frac{(\frac{80\text{x}}{3}-\frac{100\text{x}}{9})}{(\frac{100\text{x}}{9})}\times 100$
= $\frac{(\frac{240\text{x}-100\text{x}}{9})}{(\frac{100\text{x}}{9})}\times 100$
= $(\frac{140\text{x}}{9}\times \frac{9}{100\text{x}}\times 100)$
= $140\%$
Hence, the correct answer is 140%.