Discussion
The monthly incomes of A and B are in the ratio 5:6 and their monthly expenses are in the ratio 4:5, If each saves ₹ 5,000 per month, what is A's income?
Answer: B
A's income is ₹ 25,000.
Let the incomes be 5x and 6x and the expenses 4y and 5y. Each saves ₹ 5,000, so:
\[ \begin{aligned} 5x - 4y &= 5000 \\ 6x - 5y &= 5000 \end{aligned} \]
Multiply the first equation by 5 and the second by 4, then subtract to remove y:
\[ \begin{aligned} 25x - 20y &= 25000 \\ 24x - 20y &= 20000 \\ x &= 5000 \end{aligned} \]
So A's income is 5x = ₹ 25,000. Check: y = 5,000, so A spends ₹ 20,000 and saves ₹ 5,000; B earns ₹ 30,000, spends ₹ 25,000 and saves ₹ 5,000. ₹ 30,000 is B's income, not A's.
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