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 correct option is 161 opt a
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Answer 1

Answer :-

Let the unit digit be x, ten's digit be y and hundredths digit be z.

Number = zyx

Value = 100z + 10y + x

According to the question,

→ x + y + z = 8 -i

→ y = 3 ( z + x ) -ii

Number obtained on reversing the digits = 100x + 10y + z = 0

Now,

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

→ 100z + 10y + x - 100x - 10y - z = 0

→ 99z - 99x = 0

→ 99z = 99x

→ z = x

From equation ii :-

→ y = 3 ( z + x )

→ y = 3 ( x + x )

→ y = 3 ( 2x )

→ y = 6x

Substituting the value of y and z in equation i :-

→ x + y + z = 8

→ x + 6x + x = 8

→ 8x = 8

→ x = 1

→ y = 6 × 1 = 6

→ z = x = 1

Number = 161