Question

The sum of a two-digit number and the number obtained by reversing the order of its digits is 165. If the digits differ by 3, find the number.​

Answer 1

Given:–

• Sum of a two digit number and the number obtained by reversing the order of its digit is 165.
• The digits are differ by 3.

To Find:–

• What is the number ?

Solution:–

Let the digit at unit place be 'y' and the digit at tens place be 'x'

• NUMBER = 10x + y

${\underline{\bf{According \: To \: Question:-}}}$

❍ The sum of a two-digit number and the number obtained by reversing the order of its digits is 165.

◉ Number formed by reversing the digits = 10y + x

$\sf{\implies (10x + y) + (10y + x) = 165 }$

$\sf{\implies 11 x + 11 y = 165}$

Dividing by '11' on both sides

$\sf{\implies x + y = 15 }$

$\sf{\implies x = 15 -y...1) }$

Now,

❍ The digits are differ by 3.

$\sf{\implies x - y = 3...2)}$

On putting the value of 'x' from equation 1 in equation 2, we get

$\sf{\implies (15 - y) - y = 3 }$

$\sf{\implies -2y = 3-15 }$

$\sf{\implies -2y = -12 }$

$\sf{\implies y = \cancel\dfrac{-12}{-2}}$

${\large{\implies{\underbrace{\mathbf{\red{ \: y = 6 \: }}}}}}$

Now, put the value of 'y' in equation 1

$\sf{\implies x = 15 - 6}$

${\large{\implies{\underbrace{\mathbf{\red{ \: x = 9 \:}}}}}}$

❛ Hence, the number becomes 96 ❜

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Answer 2

${\large{\bold{\rm{\underline{Let's \; understand \; the \; question \; 1^{st}}}}}}$

This question says that the sum of a two-digit number and the number obtained by reversing the order of its digits is 165. If the digits differ by 3, we have to find the original number.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ The sum of a two-digit number and the number obtained by reversing the order of its digits is 165.

★ The digits differ by number 3.

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ The original number

${\large{\bold{\rm{\underline{Solution}}}}}$

★ The original number = 96

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ According to the question let's the unit digit be a and the ten's digit be b. The the coming number is 10b + a

~ According to the question,

➝ (10b + a) + (10a + b) = 165

➝ a + b = 15 Equation 1

➝ a - b = 3 Equation 2

➝ b - a = 3 Equation 3

~ Let us solve Equation 1 and 2

➝ a = 9

➝ b = 6

• Henceforth, the digit be 69.

~ Now let's solve Equation 1 and 3

➝ a = 6

➝ b = 9

• Henceforth, the digit be 96

• Original number = 96

${\large{\bold{\rm{\underline{Verification}}}}}$

~ According to the collected data..!

➝ 69 + 96 = 165

➝ 9 - 6 = 3

• Henceforth, both the conditions come true. Henceforth, verified..!