The ratio of the incomes of $\mathrm { A }$ and $\mathrm { B }$ is $5 : 4$ andthe ratio of their expenditures is $3 : 2 .$ If at the end of the year, each saves $\mathrm { Rs } .1600$ , then the income of $\mathrm { A }$ is :

Let the incomes of A and B be 5x and 4x respectively, and their expenditures be 3y and 2y respectively. Since both save Rs 1600, the equations are 5x minus 3y equals 1600 and 4x minus 2y equals 1600, and multiplying the second equation by 3 gives 12x minus 6y equals 4800 while multiplying the first by 2 gives 10x minus 6y equals 3200. Subtracting the two yields 2x equals 1600, so x equals 800. The income of A is 5x, which is 5 times 800. The result is Rs 4000.

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