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%
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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%.
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