Question

16. A two-digit number is such that the product of its digits is 35. If 18
is added to the number, the digits interchange their places. Find the
number
TCBSE 20061​

Answer 1

AnswEr :

57.

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

A two - digit number is such that the product of it's digit is 35. If 18 is added to the number, the digits interchange their places.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The number .

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Let the digit of ten's place be r

Let the digit of one's place be m

The original number = 10r + m

The reversed number = 10m + r

A/q

rm = 35

m = 35/r.............(1)

&

→ 10r + m + 18 = 10m + r

→ 10r -r +m-10m + 18 = 0

→ 9r - 9m + 18 = 0

→ 9(r-m + 2) = 0

→ r - m + 2 = 0

→ r - m + 2 = 0

Putting the value of m in equation (1),we get;

→ r - 35/r +2=0

→ r² -35 + 2r=0

→ r² + 2r -35 = 0

→ r² + 7r - 5r - 35 =0

→ r(r+7) - 5(r+7) = 0

→ (r+7) (r-5)=0

→ r+7=0 or r-5=0

→ r = -7 or r = 5

We know that negative value isn't acceptable.

Putting the value of r = 5 in eqution (1), we get;

→ m = 35/5

→ m = 7

Thus,

The number is 10r + m = 10(5) + 7 = 50 + 7 = 57.

Answer 2

Given:

A two-digit number is such that the product of its digits is 35. If 18

is added to the number, the digits interchange their places.

To find;

The number

Explanation;

Let the digit of ten's place be r

Let the digit of one's place be m

The original number = 1r + m

The reversed number = 10r + r

A.T.Q

rm = 35

m = 35/r ........(1)

10r + m + 10 = 10m + r

10r - r + m - 10m + 18 = 0

9r - 9m + 18 = 0

9(r - m + 2) = 0

r - m + 2 = 0

putting the value of m in equation (1), we get;

r - 35/r + 2 = 0

r² - 35 + 2r = 0

r² + 2r - 35 = 0

r² + 7r - 5r - 35 = 0

r( r + 7) -5(r + 7) = 0

( r + 7) (r - 5) = 0

r + 7 = 0 or r - 5 = 0

r =-7 or r =5

We know that negative value isn't acceptable.

putting the value of r = 5 in equation (1), we get;

m = 35/5

m = 7

Thus,

The number is 10r + m = 10(5) + 7 = 50 + 7 = 57.

silentlover45.❤️