A) 29
B) 28
C) 55
D) 95
E) None of these
Correct Answer: B
Solution :
Explanation Since the required number is a two digit number so, we have to find its units digit and tens digit. Let the digit at ones place be x. It is given that the sum of the digit of the number is 10. \[\therefore \] The digit at the tens place \[=10 - x\] Thus the Original number \[= 10 x \left( 10 - x \right) + x\] \[= 100 - 10x + x = 100 - 9x\] On interchanging the digits of the given number the digit at the ones place becomes \[\left( 10 - x \right)\] and the digit at the tens place becomes x. \[\therefore \,New number = 10x + \left( 10- x \right)=9x+ 10\] It is given that the new number exceeds the original number by 54. i.e.. New number-original number = 54 \[\left( 9x+10 \right)-\left( 100-9x \right)=54\] \[\therefore \,\,9x + 10 - 100 + 9x = 54\] Or, \[18x - 90 = 54\] \[\therefore \,18x =54+90\] Or, \[18x = 144\] Or, \[x=\frac{144}{18}=8\] \[\therefore \] The digit at the ones place \[=\text{ }8\] The digit at the tens place \[= \left( 10 - 8 \right) = 2\] \[\therefore \,Original number = 28.\]
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