Question

Plss solve the 2nd question

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ Sum of the digits of a two digit number is 12

✭ If the digits are reversed then the new number is 54 greater than the original one

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The original number?

$\displaystyle\large\underline{\sf\gray{Solution}}$

Let's assume the numbers to digits to be x & y

• Original Number = 10x+y
• On reversing = 10y+x

━━━━━━━━━

$\underline{\bigstar\:\textsf{According to the given Question :}}$

»» $\displaystyle\sf x+y = 12\:\:\: -eq(1)$

Also on reversing the digits,

➝ $\displaystyle\sf 10x+y+54 = 10y+x$

➝ $\displaystyle\sf 10x+y-10y+x = -54$

➝ $\displaystyle\sf 9x-9y = 54$

➝ $\displaystyle\sf 9(x-y) = 54$

➝ $\displaystyle\sf x-y = \dfrac{54}{9}$

➝ $\displaystyle\sf x-y = -6\:\:\: -eq(2)$

Adding eq(2) from eq(1)

›› $\displaystyle\sf x+y+x-y = 12+(-6)$

›› $\displaystyle\sf 2x = 6$

›› $\displaystyle\sf x = \dfrac{6}{2}$

›› $\displaystyle\sf \orange{x = 3}$

Substituting the value of x in eq(1)

➳ $\displaystyle\sf x+y = 12$

➳ $\displaystyle\sf y = 12-3$

➳ $\displaystyle\sf y = 12-3$

➳ $\displaystyle\sf \pink{y = 9}$

$\displaystyle\therefore\:\underline{\sf The \ Number \ will \ be \ 39}$

━━━━━━━━━━━━━━━━━━

Answer 2

$\displaystyle\large\underline{\sf\pink{Given}}$

• ✭Sum of the digits of a two digit number is 12

• If the digits are reversed then the new number is 54 greater than the original one

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

• The original number?

$\displaystyle\large\underline{\sf\gray{Solution}}$

Let us assume the numbers to digits to be x & y

Original Number = 10x+y

On reversing = 10y+x

━━━━━━━━━

$\underline{\bigstar\:\textsf{According to the given Question :}}$

»» $\displaystyle\sf x+y = 12\:\:\: -eq(1)$

Also on reversing the digits,

➝ $\displaystyle\sf 10x+y+54 = 10y+x$

➝ $\displaystyle\sf 10x+y-10y+x = -54$

➝ $\displaystyle\sf 9x-9y = 54$

➝ $\displaystyle\sf 9(x-y) = 54$

➝ $\displaystyle\sf x-y = \dfrac{54}{9}$

➝ $\displaystyle\sf x-y = -6\:\:\: -eq(2)$

Adding eq(2) from eq(1)

›› $\displaystyle\sf x+y+x-y = 12+(-6)$

›› $\displaystyle\sf 2x = 6$

›› $\displaystyle\sf x = \dfrac{6}{2}$

›› $\displaystyle\sf \orange{x = 3}$

Substituting the value of x in eq(1)

➳ $\displaystyle\sf x+y = 12$

➳ $\displaystyle\sf y = 12-3$

➳ $\displaystyle\sf y = 12-3$

➳ $\displaystyle\sf \pink{y = 9}$

$\displaystyle\therefore\:\underline{\sf The \ Number \ will \ be \ 39}$