Question

the sum of the no. and no. obtained by reversing the digit is 88. also the product of the digit is 15. find the given no. Find the no.

Answer 1

Hello,

Let the digit at ones place be y and the digit at tens place x.
So,
The number will be 10x + y

This is became of we know the digits then multiplying the digits with its place value can give us the required number.

Now,
If we reverse the number then the digit at tens place will go to ones place and of one's place will go to tens place.

So, The reversed number is equal to :-

10y +x

As per question :-

10x + y + 10y +x = 88
Or 11x + 11y = 88
Or x+y = 8......... (1)

Also,
Xy = 15
Or, x = 15/y........ (2)

Putting 2 in 1
X + y =8
Or 15/y +y = 8
Or 15+ y²/y =8
Or 15 + y² = 8y
Or y² - 8y +15 =0

After factorization we get (see in attachment)

Y = 5 and 3
Also
X = 15/y
So, x = 3 and 5
On testing by putting the values in eqn 1
We get that
If x= 5 then y = 3 and if x= 3 then y =5

This satisfies the eqn

So, the number can be 35 or 53

If the original number is 35 then reversed will be 53 and vice versa

Hope this will be helping you ✌️