One says, “Give me a hundred rupees, friend! I shall then become twice as rich as you.” The other replies, “If you give me ten rupees, I shall be six times as rich as you.” What is the amount of their (respective) capital?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → ₹40, ₹170
Let the first person have \(x\) rupees and the second \(y\) rupees. Money passed from one to the other is added to one amount and taken from the other, and each remark gives one equation.
The two remarks:
The first gets ₹100 and becomes twice as rich: \(x+100=2(y-100)\), so \(x=2y-300\) (1)
The second gets ₹10 and becomes six times as rich: \(y+10=6(x-10)\), so \(y=6x-70\) (2)
Solving (putting \(y\) from (2) into (1)):
\(x=2(6x-70)-300=12x-440\), so \(11x=440\)
The first person’s capital: \(x=40\) rupees
The second person’s capital, from (2): \(y=6\times40-70=170\) rupees