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The average run scored by Dhawan and Kohli is 79, the average run scored by Kohli and Rahane is 75, and that of Rahane and Dhawan is 59. Find the runs scored by Rahane.

Question

The average run scored by Dhawan and Kohli is 79, the average run scored by Kohli and Rahane is 75, and that of Rahane and Dhawan is 59. Find the runs scored by Rahane.

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Solution

Sure, let's solve this step by step:

  1. Let's denote the runs scored by Dhawan as D, by Kohli as K, and by Rahane as R.

  2. According to the problem, we have the following equations:

    (D + K) / 2 = 79 => D + K = 158 (equation 1)

    (K + R) / 2 = 75 => K + R = 150 (equation 2)

    (R + D) / 2 = 59 => R + D = 118 (equation 3)

  3. Now, let's add equation 1 and equation 2:

    D + K + K + R = 158 + 150 => 2K + D + R = 308

  4. And then subtract equation 3 from the result:

    2K + D + R - (R + D) = 308 - 118 => 2K = 190

  5. Finally, divide by 2 to find the runs scored by Kohli:

    K = 190 / 2 = 95

  6. Now, substitute K = 95 into equation 2 to find the runs scored by Rahane:

    95 + R = 150 => R = 150 - 95 = 55

So, Rahane scored 55 runs.

This problem has been solved

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