Question

The square of a two digit number is divided by half the number.after 36 is added to the quotient, this sum is then divided by 2. the digits of the resulting number are the same as those in the original number, but they are in reverse order. the ten's place of the original number is equal to twice the difference between its digits. what is the number?

Answer 1

Let the original number be N

Square of number = N^2
It is divided by half of N,...we get
(N^2/(N/2) = 2N

Now 36 is added to the quotient.
2N + 36

Now it is divided by 2, we get.
N + 18

In short when 18 is added to the original number, it's digits get reversed.

Now we represent N as

N = 10X + Y
where X is the tens place digit and Y is the units place digit.

N + 18 = 10Y + X
As the number gets reversed we reverse X and Y's places.

Now we write the equation.

N + 18 = 10Y + X
10X + Y + 18 = 10Y + X
9X + 18 = 9Y
X + 2 = Y

The difference in digits is. (Y-X)
Difference should be positive and from above equation we know that (Y>X) so I am taking difference as (Y-X)

The digit in tens place of original no. X

X = 2(Y-X)
3X = 2Y
X + 2 = Y
3X = 2×(X + 2)
3X = 2X + 4
X = 4

Y = X + 2
Y = 6

Thus the number is

46

Answer 2

Answer:

Step-by-step explanation:

the ten's place of the original number is equal to twice the difference between its digits

just look for option and try to solve you will get 46 as option

hence difference between unit and tenth place is=6-4=2

and 4=2*2

simple

that's

your answer