Question

In a 2 digit natural number, digit at tens place is equal to the square of digit at units place.When 54 is subtracted from the number,the digits get interchanged.Find the original number.​

Answer 1

The original number is 93

Step-by-step explanation:

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

The number is denoted as 10x + y

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

10 y2 + y – 54 = 10 y + y2

9 y2 – 54 =9y

9 y2 – 9y - 54 =0

Dividing by 9

y2 – y - 6 =0

y2 – 3y + 2y – 6 = 0

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

(y-3) (y+2) = 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