Math, asked by raparthyrajurraju461, 8 months ago

I am a three digit even number, sum of my digits is 3rd multiple of 5 ,my ones digit is biggest among the digits ,the difference of ones and hundreds digits is two,my tens digit is one more than hundred digit?​

Answers

Answered by Stera
29

Answer

The required three digit number is 456

\bf\large\underline{Given}

In a three digit number :

  • Sum of the digits is 3rd multiple of 5
  • Ones digit is biggest
  • The difference of ones and hundreds digits is 2
  • Tens digit is 1 more than hundreds digit

\bf\large\underline{To \: Find}

  • The number

\bf\large\underline{Solution}

Let us consider :

  • The hundreds digit be x
  • The tens digit be y
  • The ones digit be z

Therefore , the number is

\sf\longrightarrow 100x + 10y + z

From the given conditions we have :

\sf\bullet \: \:   x + y + z = 3\times 5 \\\\ \sf\implies x + y + z = 15 \dashrightarrow (1)

\sf \bullet \: \:  z > x , y

\sf \bullet \: \: z - x = 2 \\\\ \sf\implies z = x + 2 \dashrightarrow(2)

\sf \bullet \: \: y = x + 1 \dashrightarrow (3)

Putting the values from (2) and (3) in (1) we have :

\sf \implies x + x + 2 + x + 1 = 15 \\\\ \sf\implies 3x + 3 = 15 \\\\ \sf\implies 3x = 12 \\\\ \sf\implies x = 4

Again putting the value of x in (2) and (3)

   \sf  y = 4 + 1 \:  \: and \:  \: z = 4 + 2 \\  \\  \implies \sf y = 5 \:  \: and \:  \:  \implies \: z = 6

Thus , the required number is

  \longrightarrow\sf100 \times 4 + 10 \times 5 + 6 \\  \\  \sf \longrightarrow 400 + 50 + 6 \\  \\  \sf \longrightarrow 456

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