The average of twelve numbers is 42. The average of the last five numbers is 40, and that of the first four numbers is 44. The 6th number is 6 less than the fifth and 5 less than the 7th number. The average of the 5th and the 7th numbers is:
Show answer & explanation
Correct answer: D
Explanation
Correct answer is option 4 i.e. 44.5
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Concept |
Understanding |
Application |
Fair calculation |
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Average = Sum of numbers/Total numbers |
Let 5th number = x Then 6th number = (x – 6) 7th number = (x – 1) |
Sum of total 12 numbers = 12 × 42 = 504 Sum of last 5th number = 5 × 40 = 200 Sum of first 4 number = 4 × 44 = 176 Then, Sum of 5th, 6th and 7th number = 504 – 200 – 176 = 128 ⇒ x + x -1 + x – 6 = 128 ⇒ x = 45 |
12 × 42 = 504 5 × 40 = 200 4 × 44 = 176
504 – 200 – 176 = 504 – 376 = 128
3x = 128 + 7 3x = 135 x = 45 |
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The average of the 5th and the 7th numbers = (45 + 44)/2 = 44.5 |
(45 + 44)/2 = 89/2 = 44.5 |