The ratio of expenditure of A,B and C is 16:12:9.Their total income is Rs.1530.Find the shares of B's income if they save 20%,25% and 40% of the income.

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$$\begin{gathered} Income is either saved or spent. \\ Thus, Income = Expenditure + Saving \\ \Rightarrow Income - Saving = Expenditure \\ Let the incomes of A, B and C be x, y and z respectively. \\ Then, x + y + z = Rs. 1,530 \\ Now, A, B and C save 20\%, 25\% and 40\% of their incomes respectively. \\ Therefore, A saves = 20\% of x = \frac{20x}{100} = \frac{x}{5}; B saves = 25\% of y = \frac{25y}{100} = \frac{y}{4} and C saves = 40\% of z = \frac{40z}{100} = \frac{2z}{5} \\ Hence, A\text{'}s expenditure = x - \frac{x}{5} = \frac{4x}{5}; B\text{'}s expenditure = y - \frac{y}{4} = \frac{3y}{4} and C\text{'}s expenditure = z - \frac{2z}{5} = \frac{3z}{5} \\ Expenditure of A:B:C = 16:12:9 \\ Let the expenditures of A, B and C be 16k, 12k and 9k respectively. \\ So, \frac{4x}{5} = 16k, \frac{3y}{4} = 12k and \frac{3z}{5} = 9k \\ \Rightarrow x = 20k, y = 16k and z = 15k. \\ Now, x + y + z = 1530 \\ \Rightarrow 20k + 16k + 15k = 1530 \\ \Rightarrow 51k = 1530 \\ \Rightarrow k = 30 \\ Thus, B\text{'}s income = y = 16k = 16 \times 30 = Rs. 480 \end{gathered}$$

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