Three friends A, B and C respectively have Rs. 160, Rs. 120 and Rs. 80. They started playing a game in
which the person who has the maximum money gives to both the persons an amount equal to half the
difference between his amount and the respective person's amount. The game stops when the difference
between the amounts of any two of them has, is less than Rs.5.
what would be the amount of C at the end of the game
A- 117.5
B- 122.5
C- 115
D- 120
Answers
Answer:
117.5
Step-by-step explanation:
I cannot give proper explanation, cuz it takes more than 18 steps
Answer:
D) 120
Step-by-step explanation:
Given:- A has Rs.160, B has Rs.120 and C has Rs.80.
To Find:- Amount C has left at the end of the game.
Solution:-
A = 160, B = 120, C = 80.
As acc. to question, person with maximum money has to give both the person an amount equal to half the difference between his and their amount.
As we can see, A has the maximum amount.
A will give B an amount of ( 160 - 120) / 2 = 40/2 = 20.
A will give C an amount of ( 160 - 80 )/2 = 80/2 = 40.
Now, A has (160 - 20 - 40) = 100, B has (120 + 20) = 140 and C has (80+40) = 120.
Now, B has the maximum amount of 140.
B will give A and amount of ( 140 - 100)/2 = 40/2 = 20.
B will give C and amount of ( 140 - 120)/2 = 20/2 = 10.
Now, B has (140 - 20 - 10) = 110, A has (100 + 20) = 120 and C has (120 + 10) = 130.
Now, C has the maximum amount.
C will give A an amount of (130 - 120)/2 = 10/2 = 5
C will give B an amount of (130 - 110)/2 = 20/2 = 10
So, now A has (120 + 5)= 125, B has (110 + 10) = 120 and C has (130 - 15) = 115.
Now, A has maximum amount.
A will give B an amount of (125 - 120)/2 = 5/2 = 2.5
A will give C an amount of (125 - 115)/2 = 10/2 = 5.
Now, A has (125 - 7.5) = 117.5, B has (120 + 2.5) = 122.5 and C has (115 + 5) = 120.
As we can see the difference between the amount of B and C is 2.5.
Therefore, the game ends here.
A is left with Rs.117.5, B is left with Rs.122.5 and C is left with Rs.120.
The correct option is D) 120.
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