Question

The sum of the digits of three digit number is 8. the middle digit is thrice the sum of the other two digits. The difference between the number and the number obtained be reversing the digit is zero. What is the number? options (a)161 , b 242 c 192 d 125 pls explain clearly
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Answer 1

Any three digit number can be expressed as,

• 100x + 10y + z

Where, x, y & z are hundredths, tens and ones digits respectively.

For example:

145 = 100×1 + 10×4 + 5

• Where, x = 1, y = 4, z = 5

Similarly, Let the three digit number here be 100x + 10y + z where, x , y and z are hundredths, tens and ones digits respectively.

According to the question there are three statements regarding the relationship of the digits,

Case 1:

• Sum of the three digits is 8.

Also,

⇒ x + y + z = 8 ...(i)

Case 2:

• The middle digit is thrice (3 times greater) the sum of the other two digits.

⇒ Middle digit = 3 (first digit + last digit)

⇒ y = 3 (x + z) ...(ii)

From eq.(i), solving for y, we get

• y = 8 - z - x ...(iii)

Substituting value of y in eq.(ii)

⇒ 8 - z - x = 3(x + z)

⇒ 8 - z - x = 3x + 3z

⇒ 4x + 4z = 8

⇒ x + z = 2 ...(iv)

Case 3:

• The difference b/w the original number and the number obtained by reversing the digits is 0.

It can also be expressed as,

⇒ Orginal Number - (Obtained number) = 0

⇒ 100x + 10y + z - (100z + 10y + x) = 0

⇒ 100x + 10y + z - 100z - 10y - x = 0

⇒ 99x - 99z = 0

⇒ x - z = 0 ...(v)

Adding (iv) & (v), we get

⇒ x + z + x - z = 2 + 0

⇒ 2x = 2

⇒ x = 1

Substituting value of x in (v) , we get

⇒ 1 - z = 0

⇒ z = 1

Further, Substitute values of x and z in eq.(ii), we will get y as,

⇒ y = 8 - (1) - (1)

⇒ y = 8 - 2

⇒ y = 6

So, We found the digits to be 1, 6 & 1 as x, y and z. Now, Let's find the original number,

⇒ Number = 100x + 10y + z

⇒ Number = 100(1) + 10(6) + 1

⇒ Number = 100 + 60 + 1

⇒ Number = 161

Hence, The number is 161.

∴ Option (a) is correct.

Answer 2

Answer:

161

Step-by-step explanation:

the explanation is given above