Question

A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, it's digits are reversed. Find the number. (Please answer step by step I need it urgently)​

Answer 1

Answer:

The number is 35.

Step-by-step explanation:

Given :-

• A two digit number is 3 more than 4 times the sum of its digits.
• If 18 is added to the number, its digits are reserved.

To find :-

• The number.

Solution :-

Let,

• Tens digit = x
• Unit digit = y

Then,

The number = 10x + y

According to the 1st condition,

• A two digit number is 3 more than 4 times the sum of its digits.

$\to\sf{10x+y=3+4(x+y)}$

$\to\sf{10x+y=3+4x+4y}$

$\to\sf{10x-4x=3+4y-y}$

$\to\sf{6x=3+3y}$

$\to\sf{6x=3(1+y)}$

$\to\sf{2x=1+y}$

$\to\sf{y=2x-1.................(i)}$

According to the 2nd condition,

• If 18 is added to the number, its digits are reserved.

→ 10x+y+18=10y+x

→ 10x-x+y-10y=-18

→ 9x-9y=-18

→ 9(x-y)=-18

→ x-y = -2

→ x - 2x+1 = -2 [put y=2x-1 from eq(I)]

→ -x = -3

→ x = 3

Therefore,

• Tens digit = 3
• Unit digit = 2×3 -1 = 5

Then,

The number = 3×10+5 = 35

Answer 2

$\bf \large{ \underline{ \underline{ \red{Question : }}}}$

A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, it's digits are reversed. Find the number.

$\bf \large{ \underline{ \underline{ \red{Answer : }}}}$

$\sf \large \: Let \: \: the \: \: tens \: \: and \: \: units \: \: digit \: \: on \: \: number \: \: are \: \: x,y. \\ \\ \sf{ \underline{ \underline \blue{first \: \: condition : }}} \\ \\ \sf \implies \: 10x + y = 3 + 4(x + y) \\ \\ \sf \implies \: 6x - 3y = 3 \\ \\ \sf \implies \: 2x - y = 1..........(1) \\ \\ \sf{ \underline{ \underline \blue{second \: \: condition : }}} \\ \\ \sf \implies \:10x + y + 18 = 10y + x \\ \\ \sf \implies \:x - y = - 2......(2) \\ \\ \sf{ \underline{ \underline \purple{subtract \: \: eq(1) \: \: and \: \: (2): }}} \\ \\ \sf \: 2x \: \: - y \: \: = \: \: 1 \\ \\ \sf \: x \: \: \: - y \: \: \: = \: \: - 2 \\ \sf \underline{( - ) \: \: \: ( + ) = ( - )} \: \\ \sf \underline{x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: 3} \\ \\ \sf \implies \: x = 3 \: \: substitute \: \: \: in \: \: eq \: \: (2) \\ \\ \sf \implies \:x - y = - 2 \\ \\ \sf \implies \:3 - y = - 2 \\ \\ \sf \implies \: - y = - 5 \\ \\ \sf \implies \:y = 5 \\ \\ \bf { \underline{ \underline{ \green{ \therefore \: \: \: two \: \: \: digit \: \: \: number \: \: = 35 \: \: }}}}$