12. Aruna has only Re 1 and Rs 2 coins with her. If the total number of coins is 50 and the total amount is Rs 75, then the number of Re 1 and Rs 2 coins are, respectively
35 and 15
35 and 20
15 and 35
25 and 25
Step 1: Define variables.
Let the number of Re 1 coins be \(r\).
Let the number of Rs 2 coins be \(t\).
Step 2: Form equations from the conditions.
Total number of coins is 50:
\(r + t = 50\).
Total value of coins is Rs 75:
\(1 \times r + 2 \times t = 75\).
So the second equation is \(r + 2t = 75\).
Step 3: Solve the system of equations.
Subtract the first equation from the second:
\((r + 2t) - (r + t) = 75 - 50\)
\(t = 25\).
Now substitute \(t = 25\) in the first equation:
\(r + 25 = 50\)
\(r = 25\).
Step 4: Final Answer.
The number of Re 1 coins = 25, and the number of Rs 2 coins = 25.
So the correct option is (D) 25 and 25.