Income of Ais \( 60 \% \) oess than of \( B \) and expenditure of \( A \) is equal to \( 60 \% \) of the expenditure of 8 If income of \( A \) is equal to \( 70 \% \) of expenditure of \( B \). then what is the ration of savings of \( A \) and \( B \) ?
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Let's break this down! If we denote the income of B as \( x \), then the income of A is \( x - 0.6x = 0.4x \). The expenditure of B can be represented as \( y \), making A’s expenditure \( 0.6y \). According to the information given, \( 0.4x = 0.7y \). Now, we can express \( y \) in terms of \( x \): 1. \( y = \frac{0.4x}{0.7} \) 2. Plugging this into A's expenditure, we get \( 0.6y = 0.6(\frac{0.4x}{0.7}) = \frac{0.24x}{0.7} \). Next, we find the savings for both A and B: - Savings of A = Income of A - Expenditure of A = \( 0.4x - \frac{0.24x}{0.7} \) - Savings of B = Income of B - Expenditure of B = \( x - y = x - \frac{0.4x}{0.7} = \frac{0.3x}{0.7} \). Now let's find the ratio of savings of A and B: 1. Savings of A \( = 0.4x - \frac{0.24x}{0.7} \) can be calculated as: \( = 0.4x - 0.342857x \) (approx 0.343) \( = 0.05643x \) (approximately). 2. Savings of B can be expressed as \( \frac{0.3x}{0.7} \) which equals approximately \( 0.42857x \). Finally, calculating the ratio of A's savings to B's savings: \[ \text{Ratio of Savings of A to B} \approx \frac{0.05643x}{0.42857x} \approx 0.131. \] So, the ratio of savings of A and B is approximately \( 1:7.5 \). And voila! That’s how you calculate their savings!
