The monthly incomes of A and B are in the ratio of 3 : 2 and their expenditures are in the ratio of 5 : 3. Each saves Rs. 1000 a month; find their incomes.
Explanation:
Income : Ai/Bi = 3/2 Expense : Ae/Be = 5/3
Also, Ai - Ae = 1000; Bi - Be = 1000.
If I is the combined income and E the combined expense, then,
Ai = 3/5 × I, Ae = 5/8 × E, Bi = 2/5 × I, Be = 3/8 × E
It is given that, 3/5 × I - 5/8 × E = 1000 …(i)
2/5 × I - 3/8 × E = 1000 …(ii)
Solving (i) and (ii) simultaneously, E = Rs. 8,000 and I = 10,000
∴ Ai = 3/5 × 10,000 = Rs. 6,000 and Bi = 10,000 -6,000 = Rs. 4,000.
Hence, option (c).
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