Question

The digits of a two digit number differ by 3 . If the digits are interchanged and the resulting number is added to the original number, we get 143. what can be the original number​

Answer 1

Answer:

$\bigstar{\bold{Original\:number=85}}$

Step-by-step explanation:

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

• The digits differ by 3
• If the digits are interchanged and the number is added to the original number, 143 is obtained

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The original number

$\Large{\underline{\underline{\bf{Solution:}}}}$

➛ Let the unit's digit of the number be x

➛ Let the ten's digit of the number be y

➛ By given,

   y - x = 3

   y = 3 + x ------(1)

➛ Hence

   The original number = 10y + x

➛ The reversed number is given by,

    Reversed number = 10x + y

➛ By given,

   10y + x + 10x + y = 143

   11x + 11y = 143

➛Substitute the value of y in equation

  11x + 11(3 + x) = 143

  11x + 33 + 11x = 143

  22x = 110

       x = 110/22

       x = 5

➛ Hence the unit's digit of the number is 5

➛ Substitute the value of x in equation 1

   y = 3 + 5

   y = 8

➛ Hence ten's digit of the number is 8

➛ Therefore,

    Original number = 10y + x

    Original number = 10 × 8 + 5

    Original number = 85

➛ Hence the original number is 85

   $\boxed{\bold{Original\:number=85}}$

$\Large{\underline{\underline{\bf{Verification:}}}}$

➛ x - y = 3

   8 - 5 = 3

   3 = 3

➛ Original number + Reversed number = 143

   10y + x + 10x + y = 143

   10 × 8 + 5 + 10 × 5 + 8 = 143

   85 + 58 = 143

   143 = 143

➛ Hence verified.

Answer 2

Answer :-

✳ The original number = 85

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★ Question :-

The digits of a two digit number differ by 3 . If the digits are interchanged and the resulting number is added to the original number, we get 143. what can be the original number.

______________________________

★ Concept :-

Here the concept of Linear Equations in Two Variables is used. According to this, if we make the value of one variable depend on other, we can find out the value of both the variables.

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★ Solution :-

Given,

• The difference between the digits = 3

• Sum of new number and original number = 143

» Let the unit place digit in original number be x

and let the tens place digit in original number be y. Also, y > x. Then,

☞ Original Number = 10y + x

☞ New number after interchanging the digits = 10x + y

According to the question,

~ Case I :-

▶y - x = 3

▶ y = 3 + x ... (i)

~ Case II :-

▶ 10x + y + 10y + x = 143

▶11x + 11y = 143

Dividing each term, both the sides, we get,

▶ x + y = 13 ... (ii)

From equation (i) and equation (ii), we get,

✏ x + 3 + x = 13

✏ 2x + 3 = 13

✏ 2x = 13 - 3

✏ 2x = 10

✏ $</strong><strong> </strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>l</strong><strong>d</strong><strong>{</strong><strong>x</strong><strong>}</strong><strong> = </strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>l</strong><strong>d</strong><strong>{</strong><strong>\</strong><strong>d</strong><strong>frac{</strong><strong>1</strong><strong>0</strong><strong>}{</strong><strong>2</strong><strong>}</strong><strong>}</strong><strong>$

✏ x = 5

Hence, unit digit = x = 5.

Now from equation (i) , we get,

✏ y = 3 + x

✏ y = 3 + 5 = 8

✏ y = 8

Hence, tens place = y = 8

________________________________

• Orginal Number = 10y + x = 10(8)+5 = 85

• New Number = 10x + y = 10(5)+8 = 58

______________________

★ More to know :-

• Linear Equations can be solved by :-

1. Substitution Method
2. Elimination Method
3. Reducing the Pair
4. Cross Multiplication

• The graph of this word problem intersects the x axis at 5 and y axis at 8.

___________________________

★ Verification :-

In order to verify this problem, we must simply equate the values we got into the equations formed by us.

=> y - x = 3

=> 8 - 5 = 3

=> 3 = 3

Clearly, LHS = RHS.

=> 10x + y + 10y + x = 143

=> 10(5) + 8 + 10(8) + 5 = 143

=> 50 + 8 + 80 + 5 = 143

=> 143 = 143

Clearly, LHS = RHS.

Here both the conditions satisfy so the answer we got is correct.