11. The digits of a two-digit number differ by 3. If digits are interchanged and the
resulting number is added to the original number, we get 121. Find the original
number.

Question

11. The digits of a two-digit number differ by 3. If digits are interchanged and the resulting number is added to the original number, we get 121. Find the original number.​

Elliana · Answer

Answer:    Given   :  -   The digits of a two-digit number differ by 3. If digits are interchanged and the  resulting number is added to the original number, we get 121   To   Find   :  -   Original number   Solution     :  -   Let us assume that the digit at unit place is x.  Now  The tens digit is will be 3 more than it. So, the digit becomes x + 3     According to the question     sf  : Number =  bigg( 10(x + 3)  bigg) + x      sf  : Number = 10x + 30 + x      sf  : Number = (10x + x) + 30      sf  : Number = 11x + 30   When the number interchange       sf  : Interchanged  :  Number = 10 + (x + 3)      sf  : Interchanged  :  Number = (10x + x) + 3      sf  : Interchanged  :  Number = 11x + 3   Adding both the equation     sf  : (11x + 30) + (11x + 3)  = 121      sf  : (11x + 11x) + (30 + 3) = 121      sf  : 22x + 33 = 121      sf  : 22x = 121 - 33      sf  : 22x = 88      sf  : x =   cancel  dfrac{88}{22}       sf  : x = 4   Now  The tens digit = 4 + 3 = 7    Hence  The number is 74

Ariana · Answer

❍  Let's say, that the one's place digit be  y  and ten's place digit be  x  respectively.     Original number =  (10x + y).       ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀     Given that,      As per given condition, the digits of a two – digit number is differ by  3 .     Then,    ➟ x – y = 3  ➟  x = y + 3⠀⠀⠀⠀⠀  ⠀  ⠀⠀⠀  ⠀  —eq. ( I )   ⠀⠀⠀    underline{ bigstar : boldsymbol{According~to~ the~Question :}}   ⠀⠀⠀   If digits are interchanged and the resulting number is added to the original number, we get  121 .    ⠀⠀⠀  Therefore,  ⠀⠀⠀    dashrightarrow sf 10x + y + 10y + x = 121        dashrightarrow sf 11x + 11y = 121        dashrightarrow sf  x + y = 11       dashrightarrow sf y + 3 + y = 11 qquad quad bigg lgroup sf From ;eq^{n} ;1 bigg rgroup       dashrightarrow sf  2y + 3 = 11       dashrightarrow sf 2y = 11 - 3        dashrightarrow sf 2y = 8       dashrightarrow sf  y =  cancel dfrac{8}{2}       dashrightarrow underline{ boxed{ frak{ pink{ pmb{ purple{y = 4}}}}}} ; bigstar     ⠀⠀⠀  ⠀⠀⠀  underline{ bf{ dag}  : mathfrak{Putting ; value  ;of ; y  ;in ;eq^{n} ;(1) : :}} ⠀⠀⠀⠀  ⠀⠀⠀    dashrightarrow sf x = y + 3       dashrightarrow sf  x = 4 + 3       dashrightarrow boxed{ frak{ pink{ pmb{ purple{x = 7}}}}} ; bigstar        ✰     ORIGINAL NO.   =     (  1  0  x     +     y)     ✰   ⠀⠀⠀  ⇥ No. = 10x + y  ⇥ No. = 10(7) + 4  ⇥ No. = 70 + 4   ⇥     No. = 74      ⠀⠀⠀  ∴ Hence, the required two – digit  no . is  74 .         rule{250px}{.3ex}       V E R I F I C A T I O N :       As it is given that, the digits of a two– digit number is differ by  3 .     Therefore,     : implies sf x - y = 3       : implies sf 7 - 4 = 3       : implies underline{ boxed{ frak{ 3 = 3}}}    ⠀⠀⠀    qquad quad therefore{ pink{ underline{ textsf{ textbf{Hence, Verified!}}}}}

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11. The digits of a two-digit number differ by 3. If digits are interchanged and the
resulting number is added to the origina

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