Math, asked by sujeetr, 3 months ago


A two digit number is four times the sum of its digits and twice the product of its digits. Find the number. ​

Answers

Answered by pandaXop
163

Number = 36

Step-by-step explanation:

Given:

  • A two digit number is 4 times the sum of its digits.
  • Also it is 2 times the product of its digits.

To Find:

  • What is the number ?

Solution: Let ten's digit be x and unit's digit be y. Therefore ,

➟ Sum of digits = x + y

➟ Product of digits = xy

➟ Number = 10 × x + y = 10x + y

A/q

  • 10x + y = 4(x + y)

\implies{\rm } 10x + y = 4x + 4y

\implies{\rm } 10x 4x = 4y y

\implies{\rm } 6x = 3y

\implies{\rm } 2x = yㅤㅤㅤㅤi

Also ,

  • 10x + y = 2xy

\implies{\rm } 10x + y = 2x × 2x

\implies{\rm } 10x + 2x = 4x²

\implies{\rm } 12x = 4x²

\implies{\rm } 12 = 4x

\implies{\rm } 3 = x

Putting the value of x in eqⁿ i

➮ 2 × 3 = y

➮ 6 = y

So ten's digit is 3 and unit's digit is 6. Hence, the number is 36.

Answered by MяMαgıcıαη
147

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Question :

  • A two digit number is four times the sum of its digits and twice the product of its digits.

Required Answer :

  • The number is 36.

ㅤㅤㅤㅤㅤㅤ━━━━━━━━━━

Step by step explanation :

Let :

  • The ten's digit be m and unit's digit be n.

ㅤㅤㅤㅤㅤㅤ━━━━━━━━━━

  • Sum of digits = m + n
  • Product of digits = mn
  • The Number = 10(m) + n = 10m + n

Atq,

➵ㅤㅤㅤ10m + n = 4(m + n)

➵ㅤㅤㅤ10m - 4m = 4n - n

➵ㅤㅤㅤ6m = 3n

➵ㅤㅤㅤ2m = nㅤㅤㅤㅤㅤㅤ ㅤ[1]

And,

➡ㅤㅤㅤ10m + n = 2mnㅤㅤㅤㅤ[2]

From [1] putting in [2] :

➡ㅤㅤㅤ10m + 2m = 2m × 2m

➡ㅤㅤㅤ12m = 4m²

➡ㅤㅤㅤ12/4 = m²/m

➡ㅤㅤㅤm = 3

Putting value of m in equation [1] :

➢ㅤㅤㅤ2 × 3 = n

➢ㅤㅤㅤn = 6

So, ten's digit = 3 , unit's digit = 6

The number is 36

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