Answer:

16.Answer: Numbers are 57 and 75.

Step-by-step explanation:

Let the unit digit be 'x'

Let the TEN's digit be 'y'.

Original number will be

\begin{lgathered}10\times \text{ten's digit}+one's\ digit\\\\=10x+y\end{lgathered}

10×ten’s digit+one

′

s digit

=10x+y

On interchanging of digits,

Let unit's digit be 'y'.

Let ten's digit be 'x'.

New number will be

\begin{lgathered}10\times \text{ten's digit}+one's\ digit\\\\=10y+x\end{lgathered}

10×ten’s digit+one

′

s digit

=10y+x

According to QUESTION,

Product of digit of two digit number = 35

So, it BECOMES,

xy=35-----------(1)xy=35−−−−−−−−−−−(1)

If we add 18 to the number the new number obtained is number formed by interchange of digits.

17.

Answer:

Let the two - digit number be xy (i.e. 10x + y).

After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).

According to question -

xy = 18

⇒ x = 18/y.....(1)

and,

(10x + y) - 63 = (10y + x)

⇒ 9x - 9y = 63

⇒ x - y = 7.....(2)

Substituting the value of x in equation (2), we GET -

⇒ 18 - y2 = 7y

⇒ y2 + 7y - 18 = 0

⇒ y2 + 9y - 2y - 18 = 0

⇒ y(y + 9) - 2(y + 9) = 0

⇒ (y + 9)(y - 2) = 0

∴ y = 2

[y = - 9 is INVALID because digits of a number cannot be negative.]

Substituting the value of y in equation (1), we get -

x = 9

Thus, the required number is 92.