Question

Sum of the digits of two number is 5 when we interchange the digits it found that new number is less than original number by 27 what is the two digit number.

Answer 1

$\huge\sf\pink{Answer}$

☞ The original number is 41

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$\huge\sf\blue{Given}$

✭ Sum of a two digit number is 5

✭ When the digits are interchanged the new number is 27 less than the original Number

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$\huge\sf\gray{To \:Find}$

◈ The two digit number?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Let}}$

• Original Number be 10x+y
• New Number be 10y+x

☯ $\sf \underline{\boldsymbol{As \ Per \ the \ Question}}$

➠ $\sf x+y = 5$

➠ $\sf x = 5-y\:\:\: -eq(1)$

Also given that,

➝ $\sf 10y+x+27 = 10x+y$

➝ $\sf 10y+x-10x-y = -27$

➝ $\sf 9y-9x = -27$

➝ $\sf 9(y-x) = -27$

➝ $\sf y-x = \dfrac{-27}{9}$

➝ $\sf y-x = -3\:\:\: -eq(2)$

Substituting the value of eq(1) in eq(2)

➳ $\sf y-(5-y) = -3$

➳ $\sf y-5+y = -3$

➳ $\sf 2y = -3+5$

➳ $\sf 2y = 2$

➳ $\sf y = \dfrac{2}{2}$

➳ $\sf \green{y = 1}$

Substituting the value of y in eq(1)

➢ $\sf x = 5-y$

➢ $\sf x = 5-1$

➢ $\sf \red{x = 4}$

Do the original number will be,

»» $\sf Original \ Number = 10x+y$

»» $\sf Original \ Number = 10(4)+1$

»» $\sf Original \ Number = 40+1$

»» $\sf \orange{Original \ Number = 41}$

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Answer 2

Answer:

GIVEN:

Sum of the digits of a two-digit number is 5.

When we interchange the digits, the resulting new number is less than the original number by 27.

TO FIND:

What is the original number ?

SOLUTION:

Let the digit at ten's place be 'x' and the digit at unit's place be 'y'

✧ NUMBER = 10x + y

CASE:- 1)

✍ Sum of the digits of a two-digit number is 5.

According to question:-

➾ x + y = 5....❶

➾ x = 5 –y

CASE:- 2)

✍ When we interchange the digits, the resulting new number is less than the original number by 27.

✦ Reversed Number = 10y + x

✦ Reversed Number = Original Number –27

According to question:-

➾ 10y + x = 10x + y –27

➾ 27 = 10x + y –10y –x

➾ 27 = 9x –9y

Take common 9 from both sides

➾ 3 = x –y....❷

Put the value of 'x' from equation 1) in equation 2)

➾ 3 = 5 –y –y

➾ 3 = 5 –2y

➾ 3 –5 = –2y

➾ –2 = –2y

➾ y = $\sf{\cancel\dfrac{-2}{-2}} </p><p>$

❬ y = 1 ❭

Put the value of 'y' in equation 1)

➾ x + 1 = 5

➾ x = 5 –1

❬ x = 4 ❭

◉ NUMBER = 10x + y

◉ NUMBER = 10(4) + 1

◉ NUMBER = 40 + 1

◉ NUMBER = 41

❝ Hence, the number formed is 41 ❞

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