Question

A number consists of 2 digits whose sum is 4, if 18 is added to the
number, the digits get interchanged. Find the number.​

Answer 1

Step-by-step explanation:

see the answer in picture

Answer 2

$\bf{\huge{\underline{\boxed{\sf{\green{Answer:}}}}}}$

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

• A number consists of 2 digits whose sum is 4
• If 18 is added to the
• number, the digits get interchanged

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

• The number

$\bf{\underline{\underline{\sf{\red{Solution:}}}}}$

Let the digit in the tens place be x.

Let the digit in the units place be y.

Original number = 10x + y

$\bf{\underline{\underline{\sf{\red{As\:per\:first\:condition:}}}}}$

• A number consists of 2 digits whose sum is 4

Representing the condition mathematically.

=> x + y = 4

$\bf{\underline{\underline{\sf{\red{As\:per\:second\:condition:}}}}}$

• If 18 is added to the
• number, the digits get interchanged

Reversed number = 10y + x

Representing the second condition mathematically.

=> 10x + y + 18 = 10y + x

=> 10x - x + 18 = 10y - y

=> 9x + 18 = 9y

=> 9x - 9y = - 18

=> 9 ( x - y) = - 18

=> x - y = $\large\frac{-18}{9}$

=> x - y = - 2 ----> 2

Solve equations 1 and 2 simultaneously by elimination method.

Add equation 1 to equation 2,

x + y = 4

x - y = - 2

-----------------

2x = 2

=> x = $\large\frac{2}{2}$

=> x = 1

Substitute x = 1 in equation 2,

=> x - y = - 2

=> 1 - y = - 2

=> - y = - 2 - 1

=> - y = - 3

=> y = 3

$\bf{\large{\underline{\boxed{\sf{\green{Digit\:in\:the\:units\:place\:=\:x\:=\:1}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\green{Digit\:in\:the\:units\:place\:=\:y\:=\:3}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\green{Original\:number \:=\:10x\:+\:y\:=\:10\times\:1\:+3\:=\:10\:+3\:=\:13}}}}}}$

$</p><p>\bf\large\underline{Verification:}$

For first case :-

• A number consists of 2 digits whose sum is 4

Tens digit = x = 1

Units digit = y = 3

=> x + y = 4

=> 1 + 3 = 4

=> 4 = 4

LHS = RHS

For second case :-

• If 18 is added to the
• number, the digits get interchanged

Original Number = 13 = 10x + y

=> 10x + y + 18 = 10y + x

Substitute suitable values of x and y,

=> 13 + 18 = 10 ( 3) + 1

=> 13 + 18 = 30 + 1

=> 31 = 31

LHS = RHS

Hence verified.