Question

In a two digit natural number, the digit at the tens place is equal to the square of the digit at units place. If 54

is subtracted from the number, the digits get interchanged. Find the number​

Answer 1

Answer:

The original number is 93

Step-by-step explanation:

Assume that the digit in the tens place is x; while the digit in the unit place is y.

The number is denoted as 10x+y

Also, digit at tens place is square of digit at unit place

Thus;

X= y2 ................ (1)

When 54 is subtracted from the number; the digits are reversed

10x+y-54=10y+x.................(2)

Combining Eqs 1 and 2

10y2+y-54= 10y+y2

9y2 - 9y-54= 0

Dividing by 9

y2-y-6= 0

y2-3y+2y-6= 0

y(y-3)+2(y-3)= 0

Thus, y=3 or y=-2

Since it is a natural number; y cannot be -2

Hence; y=3

The digit at the tens place is square of the digit at the units place

Hence, x= 9

The original number is 93.

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