There are three numbers. If the average of any two of them is added to the third number, the sums obtained are 177, 163 and 138. What is the average of the largest and the smallest of the given numbers?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 76
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Understanding |
Application |
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Let numbers are a, b and c: Given (a + b)/2 + c = 177 (b + c)/2 + a = 163 (a + c)/2 + b = 138
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Given equations can be converted as: a + b + 2c = 354 ---- (1) b + c + 2a = 326 ---- (2) c + a + 2b = 276 ---- (3) Adding all equations: ⇒ 4(a + b + c) = 956 ⇒ (a + b + c) = 956/4 = 239 From equation 1, 2 and 3: c = 354 – 239 = 115 a = 326 – 239 = 87 b = 276 – 239 = 37 Average of the largest and the smallest of the given numbers = (115 + 37)/2 = 76 |