12. The sum of digits of a two digi...
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12. The sum of digits of a two digit number is 9. If the digits are interchanged, the resulting nu greater than the original number by 27. What is the two-digit number?

11th - 12th Class
Maths
Solution
176
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Lot the digit at ones place ( =x ) Thenteret digit at ten's place ( =9-x ) [ text { So, the number }=10 times(9-x)+frac{x}{1} ] 1 ( 4 t ) ten's eace [ begin{array}{l} =90-10 x+x =90-9 x end{array} ] When aligits are interchanged ten's alciat ( =x ) alcigit [ =x ] Lone's digit ( =9-x ). So, the mumber becomes [ begin{array}{l} =10 times 20+9-x =10 x+9-x =9 x+9 end{array} ] According fo given condition ( (9 x+9)^{prime}-(90-9 x)=27 ) ( 9 x+9-90+9 x=27 ) [ begin{array}{r} |8 x-8|=27 |8|=|27+8| 18 x=108 end{array} ] ( Rightarrow quad x=frac{108}{18} ) [ Rightarrow x=6 ] ( begin{aligned} text { The refore the two digit menuloel } i=90-9 times 6 &=90-54=36 end{aligned} )
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