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Multiplication of Negative Numbers

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Question

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Razputin has Rs. 6000 with him, which he decided to bet on 3 horses that are participating in a race. There are 5 horses participating in the race - Al, Bo, Ce, Di, and En. As per the rules of betting, the person betting on the winning horse gets four times the bet amount and those betting on the horse that came in second gets three times the bet amount. Moreover, the bet amount is returned in case the horse comes in third, and for the rest of the places, the person loses the bet amount. Razputin decided to bet Rs. 3000, Rs. 2000, and Rs. 1000 on Al, Bo and Di respectively. After the race, he notices that he ended up with no profit or loss.

At least two horses finished before En

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Al finished last

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Ce came in second

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There were three horses between Bo and Al

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Solution

The correct option is D There were three horses between Bo and Al
Total money he invested in the race is Rs. 6000. SO, in order to make no profit and incur no loss, the return from the race should also be Rs. 6000
Possible cases are = 20003; [(10004) + (20001)]; [(10003)+(3000*1)]
From the above data, the possible positions of the horses can be as follows:

Horse

Case I

Case II

Case III

Al (Rs. 3000)

4/5

4/5

3

Bo (Rs. 2000)

2

3

4/5

Ce

1/3

2/4/5

1/4/5

Di (Rs. 1000)

4/5

1

2

En

1/3

2/4/5

1/4/5

Option d requires Bo and Al to finish 1st and 5th (not necessarily in that order), which is not a possibility.

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Similar questions

Razputin has Rs. 6000 with him, which he decided to bet on 3 horses that are participating in a race. There are 5 horses participating in the race - Al, Bo, Ce, Di, and En. As per the rules of betting, the person betting on the winning horse gets four times the betting amount and those betting on the horse that came in second gets three times the betting amount. Moreover, the bet amount is returned in case the horse comes in third, and for the rest of the places, the person loses the betting amount. Razputin decided to bet Rs. 3000, Rs. 2000, and Rs. 1000 on Al, Bo and Di respectively. After the race he notices that he ended up with no profit or loss.

Q. If it is known that Ce came in fourth, then which of the following cannot be true?

राजपुतिन के पास 6000 रु. है, जिसे उसने दौड़ में भाग लेने वाले 3 घोड़ों पर दांव लगाने का फैसला किया है। दौड़ में 5 घोड़े भाग ले रहे हैं - Al, Bo, Ce, Di और En। सट्टे के नियम के अनुसार जीतने वाले घोड़े पर सट्टा लगाने वाले को सट्टे की राशि का चार गुना और दूसरे स्थान पर आने वाले घोड़े पर सट्टा लगाने वालों को सट्टे की राशि का तीन गुना राशि मिलेगा। इसके अलावा, घोड़े के तीसरे स्थान पर आने की स्थिति में सट्टे की राशि वापस कर दी जाती है, और अन्य स्थान हेतु व्यक्ति को सट्टे की राशि की हानि होती है। राजपुतिन ने Al, Bo, Ce पर क्रमशः 3000, रु. 2000, 1000 रुपए का सट्टा लगाने का निर्णय किया। दौड़ के बाद उसने देखा कि उसे कोई लाभ या हानि नहीं हुई।

Q. यदि यह ज्ञात हो कि Ce चौथे स्थान पर आया, तो निम्नलिखित में से कौन सा सत्य नहीं हो सकता है?

Q. Which of the following cannot be true?

Q. निम्नलिखित में से कौन सा सत्य नहीं हो सकता है?

Razputin has Rs. 6000 with him, which he decided to bet on 3 horses that are participating in a race. There are 5 horses participating in the race - Al, Bo, Ce, Di, and En. As per the rules of betting, the person betting on the winning horse gets four times the bet amount and those betting on the horse that came in second gets three times the bet amount. Moreover, the bet amount is returned in case the horse comes in third, and for the rest of the places, the person loses the bet amount. Razputin decided to bet Rs. 3000, Rs. 2000, and Rs. 1000 on Al, Bo and Di respectively. AFter the race he notices that he ended up with no profit or loss.

Q. If it is known that Ce came in fourth, then which of the following cannot be true?

राजपूतीन के पास 6000 रूपए हैं , जिनको उसने एक दौड़ में भाग लेने वाले 3 घोड़ों पर दांव लगाने का फैसला किया।

दौड़ में भाग लेने वाले 5 घोड़े हैं - अल, बो, सी, डि, और एन। दांव के नियमों के अनुसार, जीतने वाले घोड़े पर दांव लगाने वाले व्यक्ति को दांव की रकम का चार गुना और दूसरे नंबर पर आने वाले घोड़े पर दांव लगाने वालों को लगाई गई रकम का तीन गुना राशि मिलती है।

इसके अलावा, दांव राशि घोड़े के तीसरे स्थान पर आने की स्थिति में वापस मिल जाती है, और बाकी स्थान वाले व्यक्ति को रकम वापस नहीं की जाती है।

राजपूतिन ने 3000, रु, 2000, और 1000 रु क्रमशः अल, बो और डि पर दांव लगाया । दौड़ के बाद स्थिति ऐसी बनती है कि उसे न तो लाभ होता है और न ही हानि।

Q. यदि यह ज्ञात है कि सी चौथे स्थान पर रहा , तो निम्नलिखित में से कौन सा सही नहीं हो सकता है?

Q. Five horses are in a race. A person selects 2 of the horses at random and bets on them. The probability that he selected the winning horse is

P

makes a bet with

Q

8

pounds to

120

pounds that three races will be won by the three horses

A, B, C,

against which the betting is

3

2, 4

1,

and

2

1

respectively. The first race having been a on by

A

, and it being known that the second race was won either by

B

, or by a horse

D

against which the betting was

2

to 1, find the value of

P^{'} s

expectation.

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Horse	Case I	Case II	Case III
Al (Rs. 3000)	4/5	4/5	3
Bo (Rs. 2000)	2	3	4/5
Ce	1/3	2/4/5	1/4/5
Di (Rs. 1000)	4/5	1	2
En	1/3	2/4/5	1/4/5