1. A student finds the average of 10, 2 - digit numbers. If the digits of one of the numbers is interchanged, the average increases by 3.6. The difference between the digits of the 2-digit numbers is
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- By: anil on 05 May 2019 01.53 amaverage =$$frac{SumofElements}{NumberofElements}$$ Let the average of 10 two digit number be y Sum of 10 two digit number = 10 × y Now if digits of 1 number is interchanged , new average = y+3.6 This increment is because of change in digits of 1 two digit number . Sum of 10 numbers after interchanging digits = 10y + 36 Difference between the two cases = 9 × difference between digits of 1 two digit number whose digits have been interchanged and the unit digit of this number is greater than tens digit = 9 (b-a) Where " ab " is the two digit number whose digits have been interchanged. 9 (b-a) = 36 Hence , (b-a ) = 4
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Conditions :
(i) If the first digit is odd and the last digit is even, the codes for the first and last digits are to be interchanged.
(ii) If both the first and the last digits are even, both are to be coded as *.
(iii) If both the first and the last digits are odd, both are to be coded as $.215349