Question

What is the value of a two–digit number? A. The sum of the digits is 15. B. The difference of the squares of the digits is 45. C. The difference of their digits is 3.

Answer 1

Let the Two Digit Number be : TD

Given : The Sum of the Digits is 15

⇒ T + D = 15 ------------ [1]

Given : The Difference of the Digits is 3

⇒ T - D = 3   ------------ [2]

Adding Equation [1] and [2], We get :

⇒ (T + D) + (T - D) = 15 + 3

⇒ 2T = 18

⇒ T = 9

Substituting T = 9 in Equation [1], We get :

⇒ 9 + D = 15

⇒ D = 15 - 9

⇒ D = 6

⇒ The Value of the Two Digit Number is 96

Answer 2

$\huge{\underline{\mathfrak{Solution:}}}$



Let the two digit number be XY.

Sum of the digits = 15
X + Y = 15 ....(i)

Difference of the digits = 3
X - Y = 3 ....(ii)
Y = X - 3 ....(iii)

Adding Equating (i) and (ii), we get

(X + Y) + (X - Y) = 15 + 3
2X = 18
X = 9

Y + X = 15
Y + 9 = 15
Y = 15 - 9
Y = 6

So, Number is 96.