Question

The ratio between a 2 digit number and the sum of the digits of the number is 4:1 If the digit in the units place is 3 more than the digit in tens place Find the number using only one variable

Answer 1

Given,

• The Ratio between two digit number and the sum of the digits of the number is 4:1.
• If the digit in the units place is 3 more than the digits in tens place .

To Find,

• Two Digit Number

Solution :

$\implies$ Suppose the digit at the ten's place be x

And, Suppose the digit at the one's place be y

Therefore,

• Two Digit Number = 10x + y
• Sum of the digits = x + y

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• The ratio between two digit number and the sum of the digits of the number is 4:1.

$\implies \boxed{\sf{\dfrac{Two \ Digit \ Number }{Sum \ of \ the \ Digits} = \dfrac{4}{1}}}$

$\implies \sf{\dfrac{10x + y}{x + y} = \dfrac{4}{1}}$

$\implies \sf{10x + y = 4x + 4y}$

$\implies \sf{10x - 4x = 4y - y}$

$\implies \sf{6x = 3y}$

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• If the digit in the units place is 3 more than the digit in tens place.

$\implies \boxed{\sf{y = x + 3}}$

Now Put the Value of y in First Condition :

$\implies \sf{6x = 3y}$

$\implies \sf{6x = 3(x + 3)}$

$\implies \sf{6x = 3x + 9}$

$\implies \sf{6x - 3x = 9}$

$\implies \sf{3x = 9}$

$\implies \sf{x = \dfrac{9}{3}}$

$\implies \boxed{\sf{x = 3}}$

Therefore, Value of y find :

$\implies \sf{y = x + 3}$

$\implies \sf{y = 3 + 3}$

$\implies \boxed{\sf{y = 6}}$

$\star{\underline{\sf{Now, \ Find \ the \ Two \ Digit \ Number}}}$

$\boxed{\bold{\red{The \ Two \ Digit \ Number = 10x + y = 10(3) + 6 = 36}}}$

$\rule{200}2$

Answer 2

Given

Ratio b/w a two digit number & sum of digits = 4 : 1

Digit in unit's place is 3 more than digit in ten's place.

To find

Two digit numbers

Solution

Let the digit at ten's place be b & digit at unit's place be (b + 3)

⟼ Two digit number = b + 3 + 10b

⟼ Two digit number = 11b + 3

According to Question now :

➼ (11b + 3) : (b + b + 3) = 4 : 1

➼ (11b + 3) : (2b + 3) = 4 : 1

➼ (11b + 3)/(2b + 3) = 4

➼ 11b + 3 = 4(2b + 3)

➼ 11b + 3 = 8b + 12

➼ 11b - 8b = 12 - 3

➼ 3b = 9

➼ b = 9/3

➼ b = 3

Finding digit at unit's place :

➺ Digit at unit's place = b + 3

➺ Digit at unit's place = 3 + 3

➺ Digit at unit's place = 6

Now finding the number :

➪ Two digit number = 11(3) + 3

➪ Two digit number = 33 + 3

➪ Two digit number = 36

Therefore,

Two digits number = 36