Question

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 reversed. Find the number.
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Answer 1

SOLUTION:-

$\bf\underline{\underline{\green{Question:-}}}$

⠀⠀⠀⠀⠀• 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 reversed ⠀⠀⠀⠀⠀Find the number?

$\bf\underline{\underline{\purple{Answer:-}}}$

⠀⠀⠀⠀⠀• Required number is 35

$\bf\underline{\underline{\green{To\:Calculate:-}}}$

⠀⠀⠀⠀⠀• Number __?

$\bf\underline{\underline{\purple{Explanation:-}}}$

Let The Tens and the units digits of the Required number be x and y

Number = (10x+y)

According to question

Case 1

➺ 10x+y= 4(x+y)+3

➺ 10x+y= 4x+4y+3

➺10x-4x+y-4y=3

➺ 6x-3y=3

➺ 3(2x-y)=3

➺ 2x-y=1_________(1)

⠀Case2⠀⠀⠀

➺ 10x+y+18=10y+x

➺10x-x+y-10y=-18

➺9x-9y=-18

➺9(x-y)=-18

➺x-y=-2________(2)

On Subtracting Equation 2 from 1

2x-y=1

x-y=-2

________

x=3

➺ x= 3

Putting value of x in eq 2

x-y=-2

➺ 3-y=-2

➺-y=-2-3

➺-y=-5

➺ y= 5

Number = 10x+y

➺10×3+5

➺ 30+5

➺35

$\bf\underline{\underline{\green{Hence:-}}}$

⠀⠀⠀⠀⠀• Required Number is 35

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