# A two digit number is 4 times the sum

Asked by admin @ in **Math** viewed by 125 People

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

Asked by admin @ in **Math** viewed by 125 People

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

Answered by admin @

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

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

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