Question

A two digit number is four times the sum of its digits. If 27 were added to the number , it becomes seven times the sum of digits. Find the number.

Answer 1

Here is the Solution :

Let the 2 digit number be ab,

Where ab = 10a + b, and sum of digits be a+b,

According to the Question,

ab = 4(a+b)

=> 10a + b = 4a + 4b,

=> 6a = 3b,

=> 2a = b ---------(1),

Again, According to the Question,

ab + 27 = 7(a+b)

=> 10a + b + 27 = 7a + 7b,

=> 3a + 27 = 6b,

Dividing 3 on both sides,

=> a + 9 = 2b, --------(2),

Substituting (1) in (2),

=> a + 9 = 4a,

=> 3a = 9,

=> a = 3,

=> b = 6,

Therefore : The number is 36,,

Proof :

36 = 4(3+6),

=> 36 = 4*9 = 36, ✔,

36 + 27 = 7(3+6)

=> 63 = 7*9 = 63 ✔,

Therefore : 36 is the required number,

Hope you understand, Have a Great day :D,
Thanking you, Bunti 360 !.