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In a game between X and Y, X has to give ₹ 10 each time he loses to Y.

June 1, 2025 by rawan239

In a game between X and Y, X has to give ₹ 10 each time he loses to Y. If he wins, then he gets ₹ 50 from Y. If they play 15 times and X earns ₹ 450, how many times does X win ?

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This question was previously asked in

UPSC CISF-AC-EXE – 2023

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Let W be the number of times X wins and L be the number of times X loses. The total number of games played is W + L = 15. When X wins, he gains ₹ 50, so the total gain from wins is 50W. When X loses, he gives ₹ 10, so the total loss from losses is 10L. X’s net earning is the total gain minus the total loss, which is 50W – 10L. We are given that X earns ₹ 450, so 50W – 10L = 450. We now have a system of two linear equations: 1) W + L = 15 and 2) 50W – 10L = 450. From equation 1, L = 15 – W. Substituting this into equation 2: 50W – 10(15 – W) = 450. 50W – 150 + 10W = 450. 60W – 150 = 450. 60W = 600. W = 600 / 60 = 10. X wins 10 times.

– Define variables for the number of wins and losses.
– Set up one equation based on the total number of games played.
– Set up a second equation based on the total net earning (total gain from wins minus total loss from losses).
– Solve the system of linear equations for the number of wins.

This is an algebra word problem that requires setting up and solving a system of equations. It’s important to correctly represent the gain and loss per game and relate the total gain/loss to the net earning. Checking the answer (10 wins, 5 losses: 10*50 – 5*10 = 500 – 50 = 450) confirms the solution.

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