Question

46. A two-digit munber, when multiplied by 3, equals the square of the sum of its digits. If three times the
sum of the digits is equal to the number itself, then find the number.
{27}​

Answer 1

Answer:

the two digit number=27

Answer 2

The number is 27

Solution:

Let the unit digit be y

Let the tens digit be x

Therefore,

two digit number = 10x + y

A two-digit munber, when multiplied by 3, equals the square of the sum of its digits

According to this condition,

$3(10x + y) = (x + y)^2$ ------ eqn 1

If three times the  sum of the digits is equal to the number itself

Therefore,

3(x + y) = 10x + y

$(x+y) = \frac{10x+y}{3}$

Take square on both sides

$(x+y)^2 = ( \frac{10x+y}{3})^2 ------ eqn 2$

From eqn 1 and eqn 2,

$3(10x+y) = (\frac{10x+y}{3})^2\\\\3 = \frac{10x + y}{9}\\\\10x + y = 27$

Thus the number is 27

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