A sum of a number and the reciprocal of aggregation of 2nd, 3rd and 4th parts of the number is 1/26 more than the number. Find the number.
Let the number be X.
Then aggregation of its 2nd, 3rd and 4th parts = X/2 + X/3 + X/4 = (12X + 8X + 6X)/24 = 26X/24
And the reciprocal of aggregation of 2nd, 3rd and 4th parts of X = 1/(26X/24) = 24/26X
From the given question, we have X + 24/26X = 1/26 + X
Cancel out X on both sides, we have
24/26 X = 1/26
24 / X = 1
X = 24
Hence the required number is 24.
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