Class 9 Answered

a certain fraction has two decimal places. if the digits in these places be interchanged, the decimal fraction increases by 0.27. the sum of the digits is 9. find the fraction.

Asked by Bhawna | 04 Mar, 2015, 19:46: PM

Expert Answer

L e t space t h e space f r a c t i o n space b e space. a b W h i c h space c a n space b e space w r i t t e n space a s space fraction numerator a b over denominator 100 end fraction equals fraction numerator 10 a plus b over denominator 100 end fraction I f space d i g i t s space a r e space i n t e r c h a n g e d comma space t h e n space t h e space f r a c t i o n space b e c o m e s space fraction numerator 10 b plus a over denominator 100 end fraction fraction numerator 10 b plus a over denominator 100 end fraction minus fraction numerator 10 a plus b over denominator 100 end fraction equals.27 rightwards double arrow fraction numerator 10 b plus a over denominator 100 end fraction minus fraction numerator 10 a plus b over denominator 100 end fraction equals 27 over 100 rightwards double arrow fraction numerator 9 b minus 9 a over denominator 100 end fraction equals 27 over 100 rightwards double arrow 9 b minus 9 a equals 27 rightwards double arrow 9 left parenthesis b minus a right parenthesis equals 27 rightwards double arrow b minus a equals 3...... left parenthesis i right parenthesis T h e space s u m space o f space t h e space d i g i t s space i s space 9 b plus a equals 9...... left parenthesis i i right parenthesis left parenthesis i right parenthesis plus left parenthesis i i right parenthesis comma 2 b equals 12 rightwards double arrow b equals 6 a equals 3 therefore T h e space f r a c t i o n space i s space.36

Answered by Prasenjit Paul | 06 Mar, 2015, 10:22: AM

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