Question

Example 14: The digits of a two-digit number differ by 3. If the digits are interchange
and the resulting number is added to the original number, we get 143. What can be the
original number?​

Answer 1

AnsWer :

85.

SolutioN :

Let,

• The unit place Value be x
• The ten place Value be y.
• Original Number → 10x + y.
• Interchange number → 10y + x.

# Case 1.

• The digits of a two-digit number differ by 3.

→ x - y = 3.________( 1 )

$\rule{100}3$

# Case 2.

• If the digits are interchange and the resulting number is added to the original number, we get 143.

→ 10x + y + 10y + x = 143.

→ 11x + 11y = 143.

→ x + y = 13._______( 2 )

$\rule{100}3$

Now, We have Pair of Linear Equation.

Let solve by substitute method.

$\rule{100}3$

Taking Equation ( 1 )

→ x - y = 3

→ x = y + 3.________( 3 )

Putting the value of x in Equation ( 2 ) We get.

→ x + y = 13.

→ y + 3 + y = 13.

→ 2y + 3 = 13.

→ 2y = 10.

→ y = 5.

Now, Putting the value of y = 5. in Equation ( 3 )

→ x = y + 3.

→ x = 5 + 3.

→ x = 8.

So, Our Number become 10x + y = 80 + 5 = 85.

Therefore the the original number is 85.