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

44 this number is four ti.es the sum.of ots digit and twise the product of its digits

Answer 2

✬ Number = 36 ✬

Step-by-step explanation:

Given:

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

To Find:

• What is the number?

Solution: Let the ten's digit of number be x and unit's digit of number be y.

∴ Number will be = 10x + y

• Case 1 = Two digit number is four times the sum of its digits i.e 10x + y = 4 (x + y)

$\small\implies{\sf }$ 10x + y = 4x + 4y

$\small\implies{\sf }$ 10x – 4x = 4y – y

$\small\implies{\sf }$ 6x = 3y

$\small\implies{\sf }$ 6x – 3y = 0

$\small\implies{\sf }$ 3 (2x – y) = 0

$\small\implies{\sf }$ 2x – y = 0

$\small\implies{\sf }$ – y = – 2x

$\small\implies{\sf }$ y = 2x ..................(1)

• Case 2 = Two digit number is twice the product of its digits. i.e 10x + y = 2xy ...........................(2)

★ Putting the value of y = 2x from equation (1) in equation (2) , we get ★

$\small\implies{\sf }$ 10x + 2x = 2x (2x)

$\small\implies{\sf }$ 12x = 4x²

$\small\implies{\sf }$ 12x – 4x² = 0

$\small\implies{\sf }$ 4x ( 3 – x) = 0

$\small\implies{\sf }$ 3 – x = 0

$\small\implies{\sf }$ – x = – 3

$\small\implies{\sf }$ x = 3

Hence, The value of x = 3

• Putting the value of x in equation 1 •

• y = 2x
• y = 2 (3) = 6

Thus, The tens digit of number is x = 3 and unit's digit of number is y = 6

∴ Required number = 36