Question

A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

Answer 1

SOLUTION :

Let the digit at the tens and units place be x and y .

Two digit number = 10x + y

A T.Q

Number = 4(sum of the digits) & Number = 2(product of the digits)

10x + y = 4(x + y)                 And 10x + y = 2xy …………(1)

10x + y = 4x + 4y  

10x - 4x = 4y - y  

6x - 3y = 0  

3(2x - y) = 0  

2x - y = 0  

2x = y ……………….(2)

Put this value of y in eq 1

10x + y = 2xy

10x + 2x = 2x(2x)  

12x =  4x²

4x² - 12x = 0

4x(x - 3) = 0

4x = 0  or (x - 3) = 0

x = 0 or x = 3

Since, the given number is a two digit number so its tens digit cannot be zero ( x ≠ 0 )

Therefore , x = 3

Put this value of x in eq 2,

y = 2x

y = 2 (3)

y = 6

Required number = 10x + y  

= 10(3) + 6

= 30 + 6

Required number = 36

Hence, the Required two digit number is 36 .

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Answer 2

Sol: 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