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Grade 88 grade maths

Sum of the digits of a two digit no. is 9. when we interchange the digit it is found that the resulting new no. is greater than the orignal no. by 27. What is the two digit no. is?

Profile image of Ritesh Punia
10 Years agoGrade 8
Answers icon

1 Answer

Profile image of Ankit Jaiswal
10 Years ago
Let the 2 digit number as 
10b + a
so here the digit at tens place is b and at units plac a  
it is given that 
a + b = 9..........................(eq 1)
and 
10b + a = 10a + b + 27 
\therefore 9b – 9a = 27
\therefore 9( a - b ) = 27
\therefore a – b = 3.........................(eq 2)
now on adding eq1 and eq2
we get
a + b + a - b =3+9
\therefore 2a = 12
\therefore a = 6
 now on substituting the value of a in eq2
a – b = 3
\therefore 6 – b= 3
\therefore b = 6 – 3 = 3
therefore the number is 
10b + a = 30 + 6 = 36
if you found the solution good then please approve my answer. 
thank you
 
 

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