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In a casino, there were three different coloured tokens - Red, Green, and Blue - with face values of Rs.20, Rs.50 and Rs.100 respectively. The total worth of all the tokens in the casino was Rs.18,500. On a busy day, when the tokens were not sufficient, all the Red tokens were given a new face value of Rs.200 ( while there was no change in the value of the Green and Blue tokens). The Net worth of all the tokens after the change was Rs.27,500. If the average number of tokens per colour is equal to the number of Green tokens, then find the total number of tokens in the casino.

1. 150
2. 180
3. 270
4. 288

 Color Red Green Blue Face Value 20 50 100 Face Value on busy day 200 50 100

Let X=Number of Red Tokens

Y=Number of Green Tokens

Z=Number of Blue Tokens

Total price of all Tokens =20 X + 50 Y + 100 Z = 18500                             ........(1)

Total price of all Tokens on Busy Day= 200 X + 50 Y + 100 Z  =27500     .........(2)

Given the average number of tokens per color is equal to the number of Green tokens

Y= (X + Y + Z ) / 3

2Y=X + Z

Y =(X + Z) / 2                                                                                             .............(3)

Perform (2) - (1)

180 X = 9000

X=  50

Put The values of X and Y in (1)

20 * 50 + 50 * (50+z) /2 + 100 Z = 18500

1000 + 1250 + 25 Z + 100 Z =18500

125 Z =16250

Z=130

Put values X and Z in (3)

Y= (50 + 130 ) /2

Y=90

Total no of tokens casino= X + Y + Z = 50 + 90 + 130 = 270 Tokens

answered by (11k points) 7 12 98
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