Let the income of first person be Rs x and that of second person be Rs y.
According to the first condition, the ratio of their incomes is 9 : 7.
∴ x/y = 9/7
∴ 7x = 9y
∴ 7x – 9y = 0 …….(i)
Each person saves Rs 200.
Expenses of first person = Income – Saving
= x – 200
Expenses of second person = y – 200
According to the second condition, the ratio of their expenses is 4 : 3
∴ (x - 200)/(y - 200) = 4/3
∴ 3(x – 200) = 4(y – 200)
∴ 3x – 600 = 4y – 800
∴ 3x – 4y = – 800 + 600
∴ 3x – 4y = -200 …(ii)
Multiplying equation (i) by 4,
28x - 36y = 0 …(iii)
Multiplying equation (ii) by 9,
27x - 36y = -1800 …(iv)
Subtracting equation (iv) from (iii),
Substituting x = 1800 in equation (i),
7x – 9y = 0
∴ 7(1800) – 9y = 0
∴ 9y = 7 x 1800
∴ y = (7 x 1800)/9
y = 7 x 200
∴ y = 1400
∴ The income of first person is Rs 1800 and that of second person is Rs 1400.
