Question

the number of the digits of two digit is 8 if its digits are reversed the new no. 80 formed is increased by 18 find the number

Answer 1

Correct question : The sum of digits of a two digit number is 8. If the digits are reversed, the new number so formed is increased by 18. Find the number.

Answer:

Number = 35

Step-by-step explanation:

Let the digit at the tens place be x and the digit at the units place be y.

★ $\boxed{\bf \therefore Original \: number = 10x + y}$

Also, it is given that the sum of the digits is 8.

⇒ x + y = 8     ..... (i)

According to the question,

If the digits are reversed, the new number so formed is increased by 18.

$\tt \implies 10y + x = 10x + y + 18 \\\\\tt \implies 10y - y + x - 10x = 18\\\\\implies \tt 9y - 9x = 18 \\\\\implies \tt - 9 (x - y) = 18\\\\\implies \tt x - y = -\dfrac{18}{9}\\\\\implies \tt x - y = - 2\:\:\:.. (ii)$

Adding equation (i) and (ii),

$\tt \implies x + y + x - y = 8 - 2\\\\\tt \implies 2x = 6\\\\\tt \implies x = \dfrac{6}{2}\\\\\boxed{\bf \therefore x = 3}$

Substituting the value of x in (i),

$\tt \implies x + y = 8\\\\\tt \implies 3 + y = 8 \\\\\tt \implies y = 8 - 3 \\\\\ \boxed{\bf \therefore y = 5}$

Now, Original number = 10x + y

                                     = 10 * 3 + 5

                                     = 30 + 5

                                     = 35

Hence, the required number is 35.

Answer 2

Appropriate Question :

• The sum of the digits of two digit number is 8. If its digits are reversed the new number formed is increased by 18. Find the number.

Given :

• The sum of digit of a two digit number is 8.
• When the digits are reversed the new number is increased by 18.

To Find :

• The Two Digit Number

Solution :

Let the digit at the tens place be x.

Let the digit at the units place be y.

Original Number = (10x + y)

Case 1 :

The sum of tens dight and units digit is 8.

Equation :

$\longrightarrow$ $\sf{x+y=8}$

$\sf{x=8-y\:\:\:(1)}$

Case 1 :

The reversed dight is increased by 18 when the digits of the two digit number is altered.

Equation :

$\longrightarrow$ $\sf{10y+x=10x+y+18}$

$\longrightarrow$ $\sf{10y+8-y=10(8-y) +y+18}$

$\bold{\big[From\:equation\:(1)\:x\:=\:8-y\big]}$

$\longrightarrow$ $\sf{9y+8=80-10y+y+18}$

$\longrightarrow$ $\sf{9y+8=80-9y+18}$

$\longrightarrow$ $\sf{9y+8=98-9y}$

$\longrightarrow$ $\sf{9y+9y=98-8}$

$\longrightarrow$ $\sf{9y+9y=90}$

$\longrightarrow$ $\sf{18y=90}$

$\longrightarrow$ $\sf{y=\dfrac{90}{18}}$

$\longrightarrow$ $\sf{y=5}$

Substitute, y = 5 in equation (1),

$\longrightarrow$ $\sf{x=8-y}$

$\longrightarrow$ $\sf{x=8-5}$

$\longrightarrow$ $\sf{x=3}$

$\large{\boxed{\bold{Ten's\:Digit\:=\:x\:=\:3}}}$

$\large{\boxed{\bold{Units's\:Digit\:=\:y\:=\:5}}}$

$\large{\boxed{\bold{Original\:Number\:=\:10x+y=10(3)+5=30+5=35}}}$