Question

In a casino, there are three coloured tokens — Red (₹20), Green (₹50), Blue (₹100). Total worth ₹18,500. On a busy day, all Red tokens were upgraded to ₹200 (no change in Green/Blue). New worth: ₹27,500. Average number of tokens per colour equals the number of Green tokens. Find the total number of tokens.

• A. 150
• B. 180
• C. 270
• D. 288

Hint:

Translate "average equals a given variable" to an equation, then use given worths to set up a solvable system.

Answer 1

The Correct Option is C

Let $R, G, B$ = number of red, green, blue tokens. Average per colour equals $G$: \[ \frac{R+G+B}{3} = G \quad \Rightarrow \quad R + G + B = 3G \quad \Rightarrow \quad R+B = 2G \] Initial worth: \[ 20R + 50G + 100B = 18500 \] After change (Red → ₹200): \[ 200R + 50G + 100B = 27500 \] Subtract equations: \[ 180R = 9000 \quad \Rightarrow \quad R = 50 \] Then $B = 2G - R = 2G - 50$. Substitute in first worth equation: \[ 20(50) + 50G + 100(2G - 50) = 18500 \] \[ 1000 + 50G + 200G - 5000 = 18500 \] \[ 250G - 4000 = 18500 \quad \Rightarrow \quad 250G = 22500 \quad \Rightarrow \quad G = 90 \] $B = 2(90) - 50 = 130$. Total: $R+G+B = 50 + 90 + 130 = 270$. \[ \boxed{270} \]