1.

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»

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☞ 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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