Question

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

Answer 1

Gɪᴠᴇɴ :-

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

digits.

ᴛᴏ ғɪɴᴅ :-

• Number

sᴏʟᴜᴛɪᴏɴ :-

Let the digit at tens place be x and ones place be y

then,

➨ Number = (10x + y)

➢ According to 1st condition :-

• Number = 4(sum of it's digits)

➭ 10x + y = 4(x + y)

➭ 10x + y = 4x + 4y

➭ 10x - 4x + y - 4y = 0

➭ 6x - 3y = 0

➭ 3(2x - y) = 0

➭ 2x - y = 0/3

➭ 2x - y = 0

➭ y = 2x. ---(1)

➢ According to 2nd condition :-

• Number = 2(Product of it's digits)

➭ 10x + y = 2(xy)

➭ 10x + y = 2xy. --(2)

Put the value of (1) in (2), we get,

➭ 10x + y = 2xy

➭ 10x + (2x) = 2x(2x)

➭ 12x = 4x²

➭ 4x(3x) = 4x(x)

➭ 3= x

➭ x = 3

Put x = 3 in (1) , we get,

➭ y = 2x

➭ y = 2×3

➭ y = 6

Hence,

• Tens place digit = x = 3
• Ones place digit = y = 6

Therefore,

• Number is (10x + y) = 36

Answer 2

$\large\bf\underline{Solution:-}$

★ Let the digits be x and y

★ Let x is in the tens place then it sill become 10x ★ let y is in once place the it will become 1y

★ The original number be 10x+y

From the question

• 10x+y=4(x+y)
• 10x+y=4x+4y
• 10x-4x+y-4y=0
• 6x-3y=0
• 2x-y=0
• 2x=y......Eq = 1

again according to question

• 10x+y=2(xy)

substitute y=2x

• 10x+2x=2x(2x)
• 12x/2x=2x
• 6=2x
• x=3
• if x=3 then y= ?
• 2x=y
• y=6

The Number is 36 .