Question

The digit in a tens place of a 2 - digit number is twice the units digit . If the digit are reversed , the new number is 18 less than the original number . Find the original number.​

Answer 1

Given :

• Digit in tens place is twice the unit's digit.
• If digits reversed, new number is 18 less than the original number.

To find :

• Original number

Solution :

Let the digit at unit place be y and digit at ten's place be 2y [∵ Digit at tens place = twice the digit at units place]

∴ Original number = y + 10(2y) = y + 20y = 21y

Now if digits are reversed, then :

∴ New number = 2y + 10y = 12y

Now atq,

⇒ 12y = 21y - 18

⇒ 12y - 21y = - 18

⇒ -9y = -18

⇒ y = -18/-9

⇒ y = 2

∴ Digit at units place = y = 2

∴ Digit at tens place = 2y = 2(2) = 4

∴ Original number = 21y

                               = 21(2)

                               = 42

Therefore,

Original number = 42

Answer 2

Answer :-

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of the Linear Equations in Two Variables has been used. According to this, if the value of one variable is made to depend on other, then we can find both the values. Here we are taking the Unit's place and Ten's place as unknown variables and then let's find them.

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★ Question :-

The digit in a tens place of a 2 - digit number is twice the units digit . If the digit are reversed the new number is 18 less than the original number . Find the original number.

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★ Solution :-

Given,

» The digit at tens place = 2 × The digit at once place

» The original number = 18 + The new number

• Let the unit place digit be 'x'

• Let the tens place digit be 'y'

So,

» The original number = 10y + x

» The new number = 10x + y

Then, according to the question :-

~ Case I :-

✒ y = 2x ... (i)

~ Case II :-

✒ 10y + x = 10x + y + 18

✒ 10y + x - 10x - y = 18

✒ 9y - 9x = 18

Dividing all the terms by 9, we get

✒ y - x = 2 ... (ii)

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

✒ 2x - x = 2

$\: \: \large{\underline{\boxed{\boxed{\bf{x \: = \: 2}}}}}$

Now using the value of x and equation (i), we get,

✒ y = 2x

✒ y = 2(4)

$\: \: \large{\underline{\boxed{\boxed{\bf{y \: = \: 4}}}}}$

Now we got the values of x and y, so,

✒ The original number = 10y + x = 10(4) + 2

= 42

✒ The new number = 10x + y = 10(2) + 4

= 24

$\: \: \: \large{\overbrace{\underbrace{\boxed{\rm{Hence, \: the \: original \: number \: is \: \underline{42}}}}}}$

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$\large{\underline{\implies{Confused? \: Don't \: worry \: let's \: verify \: it \: :-}}}$

For verification, we need to simply apply the values we got into the equations we formed. Then,

~ Case I :-

=> y = 2x

=> 4 = 2(2)

=> 4 = 4

Clearly, LHS = RHS

=> y - x = 2

=> 4 - 2 = 2

=> 2 = 2

Clearly, LHS = RHS

Here both the conditions satisfy, so our answer is correct.

Hence, Verified.

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$\: \: \: \huge{\boxed{\tt{\large{More \: to \: know \: :-}}}}$

• Polynomials are the group of equations which are formed using constant and variable terms but are of many degrees.

• Linear Equations are the equations formed using constant and variable terms but of single degrees.

• Graphical Method if we draw a graph of this, then we see that the lines intersect each other at the coordinate (2, 4).