Question
Three numbers give 290, 276 and 260 respectively when
the average of any two is added to the remaining number. What is the difference between the highest and lowest number?Solution
ATQ,
Let numbers be x, y, z. 2x + y + z = 290 × 2 = 580 x + 2y + z = 276 × 2 = 552 x + y + 2z = 260 × 2 = 520 4(x + y + z) = 580 + 552 + 520 = 1652 x + y + z = 413 x = 580 – 413 = 167 y = 552 – 413 = 139 z = 520 – 413 = 107 Required difference = 167 – 107 = 60
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