Discussion
The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs. 2,000 per month, their monthly incomes are
Answer: C
The incomes are Rs. 18,000 and Rs. 14,000.
Let the incomes be 9x and 7x and the expenditures 4y and 3y. Each saves Rs. 2,000:
\[ \begin{aligned} 9x - 4y &= 2000 \\ 7x - 3y &= 2000 \end{aligned} \]
Multiply the first by 3 and the second by 4 and subtract:
\[ \begin{aligned} 27x - 28x &= 6000 - 8000 \\ x &= 2000 \end{aligned} \]
So the incomes are 9 × 2000 = 18,000 and 7 × 2000 = 14,000 (expenditures 16,000 and 12,000, ratio 4 : 3). The other pairs have the right 9 : 7 ratio but give different savings.
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