The digits of a positive integer, having three digits are in A. P and

1.	The digits of a positive integer, having three digits are in A. P and their sum is 15.The number obtained by reversing the digits is 594 less than the original number. Find the number
Answer» AnswEr:- Three digits number = 852 $\rule{200}{2}$ Let the three digits of the number be a, a + d & a + 2d as they are in A.P ∴ Number = a + 10(a + d) + 100(a + 2d) Case 1:- ⇒ a + (a + d) + (a + 2d) = 15 ⇒ a + a + d + a + 2d = 15 ⇒ 3a + 3D = 15 ⇒ 3(a + d) = 15 ⇒ a + d = 15/3 ⇒ a + d = 5 [Eq.1] Case 2:- Number obtained by REVERSING digits:- ∴ Number = 100a + 10(a + d) + (a + 2d) According to question:- ⇒ [a + 10(a + d) + 100(a + 2d)] - [100a + 10(a + d) + (a + 2d)] = 594 ⇒ a + 10a + 10d + 100a + 200d - 100a - 10a - 10d - a - 2d = 594 ⇒ 111a + 210d - 111a - 12D = 594 ⇒ 198d = 594 ⇒ d = 594/198 ⇒ d = 3 Put this value in (Eq.1) ⇒ a + 3 = 5 ⇒ a = 5 - 3 ⇒ a = 2 $\rule{150}{1}$ ⋆ THREE DIGITS OF THE NUMBER:- ↠ First DIGIT = a = 2 ↠ Second digit = a + d = 2 + 3 = 5 ↠Third digit = a + 2d = 2 + 2(3)= 2 + 6 = 8 $\rule{150}{2}$ ⋆ THREE DIGITS NUMBER :- ⇒ Number = 2 + 10(2 + 3) + 100{2 + 2(3)} ⇒ Number = 2 + 10(5) + 100(8) ⇒ Number = 2 + 50 + 800 ⇒ Number = 852 Therefore, Three digits number = 852 .

The digits of a positive integer, having three digits are in A. P and their sum is 15.The number obtained by reversing the digits is 594 less than the original number. Find the number

Answer»

AnswEr:-

Three digits number = 852

$\rule{200}{2}$

Let the three digits of the number be a, a + d & a + 2d as they are in A.P

∴ Number = a + 10(a + d) + 100(a + 2d)

Case 1:-

⇒ a + (a + d) + (a + 2d) = 15

⇒ a + a + d + a + 2d = 15

⇒ 3a + 3D = 15

⇒ 3(a + d) = 15

⇒ a + d = 15/3

⇒ a + d = 5 [Eq.1]

Case 2:-

Number obtained by REVERSING digits:-

∴ Number = 100a + 10(a + d) + (a + 2d)

According to question:-

⇒ [a + 10(a + d) + 100(a + 2d)] - [100a + 10(a + d) + (a + 2d)] = 594

⇒ a + 10a + 10d + 100a + 200d - 100a - 10a - 10d - a - 2d = 594

⇒ 111a + 210d - 111a - 12D = 594

⇒ 198d = 594

⇒ d = 594/198

⇒ d = 3

Put this value in (Eq.1)

⇒ a + 3 = 5

⇒ a = 5 - 3

⇒ a = 2

$\rule{150}{1}$

⋆ THREE DIGITS OF THE NUMBER:-

↠ First DIGIT = a = 2

↠ Second digit = a + d = 2 + 3 = 5

↠Third digit = a + 2d = 2 + 2(3)= 2 + 6 = 8

$\rule{150}{2}$

⋆ THREE DIGITS NUMBER :-

⇒ Number = 2 + 10(2 + 3) + 100{2 + 2(3)}

⇒ Number = 2 + 10(5) + 100(8)

⇒ Number = 2 + 50 + 800

⇒ Number = 852

Therefore,