Riya and Neha have certain amount of money. If Riya gives ₹20 to Neha, then Riya will have three times as much money as Neha. However, if Neha gives ₹40 to Riya, then Riya will have five times as much money as Neha. What is the total amount of money (in ₹) that Riya and Neha initially had together?
720
Let Riya have \(R\) rupees and Neha have \(N\) rupees.
If Riya gives ₹20 to Neha: \(R - 20 = 3(N + 20)\), which gives \(R - 20 = 3N + 60\), so \(R - 3N = 80\).
If Neha gives ₹40 to Riya: \(R + 40 = 5(N - 40)\), which gives \(R + 40 = 5N - 200\), so \(R - 5N = -240\).
Subtract the equations: \((R - 3N) - (R - 5N) = 80 - (-240)\), giving \(2N = 320\), so \(N = 160\).
Then \(R = 80 + 3N = 80 + 480 = 560\).
Total \(= R + N = 560 + 160 = 720\).
Hence, together they initially had ₹720.
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