Question 20

# Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 and Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true?

Solution

There are total 3 cases which satisfies the condition "no profit and no loss."

Case 1: White comes 2nd.(remaining two horses(red/black) come 4th/5th)

Profit from white horse = Final Amount - Initial Amount = 2000*3 - 2000 = 4000

Loss from Red and Black horse = 3000+1000 = 4000

Net profit = 4000-4000 = 0

Case 2: Black, Red come second, third respectively.(remaining one horse(white) comes 4th/5th)

Profit from Black = 1000*3-1000 = 2000

Profit from Red = 3000 - 3000 = 0

Loss from white = 2000

Net profit = 2000-2000 = 0

Case 3: black, white come first, third respectively.(remaining one horse(red) comes 4th/5th)

Profit from Black = 1000*4-1000 = 3000

Profit from White = 2000 - 2000 = 0

Loss from Red = 3000

Net Profit = 3000-3000=0

And it is mentioned that grey case 4th. ==> case 1 is wrong.(because, in that case red, black should come 4th,5th)

So option C cannot be true.

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