Question

A two digit number is such that the product of the digits is 14.When 45 is added to the
number, the digits interchange their places. Find the number.​

Answer 1

Answer:

let the ones digit be x

then 10(14 -x) (as mentioned)

= 140 - 10x

number = 10a + b

so, 140 - 10x + x = 140-9x

Answer 2

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• A word problem
• In which a two digit no is given
• Their product is 14

${\sf{\green{\underline{\large{To\:find}}}}}$

• Number

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Let the no on unit place be x and tens place be y

Then no be = x+10y

Then

• Product become 14

=>xy = 14____(1)

=>x=14/y

while

• 45 added to the no the digit interchange their place

=>x+10y+45=10x+y

=>10x-x+y-10y=45

=>9x-9y=45

=>x-y=5_____(2)

¶utting value of x

=>14/y -y =5

=>14-y²=5y

=>y²+5y-14=0

=>y²+7y-2y-14=0.

=>y(y+7)-2(y+7)=0

=>(y+7)(y-2)=0

=>y=2,-7

Taking the + value

• From equation 1

=>xy=14

=>2x=14

=>x=7

Hence the no is (x+10y)=(7+20)=27