Question

The sum of the digits of a two digit number is 10 and the digit at units place is 2/3rd of the
digit at tens place. Find the number.

​

Answer 1

Given :

• The sum of the digits of a two digit number is 10 and the digit at units place is 2/3rd of the digit at tens place.

To Find :

• The required number = ?

Solution :

Let the ten's digit of two digit number be x and one's digit be y.

• The required number = 10x + y

In the question it is given that,The sum of the digits of a two digit number is 10. So, mathematically it can be expressed as :

• x + y = 10 [Equation (i)]

It is also given that,the digit at units place is 2/3rd of the digit at tens place, mathematically it can be expressed as :

• y = ⅔ x [Equation (ii)]

Now,plug in the value of y = ⅔ x from equation (ii) to equation (i) :

→ x + ⅔ x = 10

→ (2x + 3x)/3 = 10

→ 5x = 10 × 3

→ 5x = 30

→ x = 30 ÷ 5

→ x = 6

• Hence,the ten's digit of two digit number is 6.

Now,substitute the value of x = 6 in equation (ii) :

→ y = ⅔ x

→ y = ⅔ × 6

→ y = 2 × 2

→ y = 4

• Hence,the one's digit of two digit number is 4.

★ Finding the required number :

→ Required number = 10x + y

→ Required number = 10 × 6 + 4

→ Required number = 60 + 4

→ Required number = 64

• Hence,the required two digit number is 64.

Answer 2

$\huge{\underline{\sf{\red{Question}}}}$

★The sum of the digits of a two digit number is 10 and the digit at units place is 2/3rd of the digit at tens place. Find the number.

$\huge{\underline{\sf{\red{Solution}}}}$

$\huge{\sf{➝Given:-}}$

$\green{\sf{Sum~of~digits~of~a~two~digit~number = 10}}$

★Also, the digit at units place is 2/3rd of the digit at tens place!

$\huge{\sf{➠Let,}}$

• The Tens digit = x

• The Units digit = ${\sf{\frac{2}{3}\times{x}}}$

• Their Sum = $\sf{x+\frac{2x}{3}}$

$\bf{\red{➝The~Equation~Fomed:-}}$

$\leadsto{\green{\sf{x+\frac{2x}{3}=10}}}$

$\red{\tt{➝Talking~Out~The~LCM}}$

$\leadsto{\green{\sf{\dfrac{3x+2x}{3}=10}}}$

$\leadsto{\green{\sf{\frac{5x}{3}=10}}}$

$\leadsto{\green{\sf{x=\frac{10×3}{5}}}}$

$\leadsto{\green{\sf{x=6}}}$

$\bf{\red{The~Numbers~Are:-}}$

$\leadsto{\red{\tt{The~tens~digit=6}}}$

$\leadsto{\red{\tt{The~ones~digit=6×\frac{2}{3}}}}$

$\implies{\red{\tt{The~ones~digit=2×2}}}$

$\implies{\red{\tt{The~ones~digit=4}}}$

★Hence, the required two digit number is 64 .