A lady went shopping and spent half of what she had on buying hankues and gave a rupee to a beggar waitng outside the shop.She spent half of what was left on a lunch and followed that up with a 2 rupee tip. She spent half of the remaining amount on a book and 3 rupees on bus fare. When she reached home, she found that she had exactly one rupee left. How much money did she start with?
 

Asked by slkaushalsl | 5th Jun, 2014, 09:29: AM

Expert Answer:

A s s u m e space t h a t space l a d y space s t a r t e d space w i t h space R s. space x S h e space s p e n t space x over 2 a t space s h o p p i n g. R e m a i n i n g space i s space x over 2. S h e space g a v e space 1 space r u p e e space t o space b e g g a r space o u t s i d e space s h o p. space S o space n o w space r e m a i n i n g space i s space x over 2 minus 1 S h e space s p e n t space h a l f space o f space r e m a i n i n g space a t space l u n c h space w i t h space f o l l o w e d space b y space 2 space r u p e e space t i p. space S o space s h e space s p e n t space fraction numerator begin display style x over 2 end style minus 1 over denominator 2 end fraction plus 2 M o n e y space l e f t space w i t h space t h e r space a f t e r space l u n c h space i s space fraction numerator begin display style x over 2 end style minus 1 over denominator 2 end fraction minus 2 S h e space s p e n t space h a l f space o f space t h e space r e m a i n i n g space o n space b o o k space a n d space 3 space r u p e e s space o n space b u s space f a r e. space S o space m o n e y space l e f t space w i t h space h e r space i s space fraction numerator fraction numerator begin display style x over 2 end style minus 1 over denominator 2 end fraction minus 2 over denominator 2 end fraction minus 3 F i n a l l y space s h e space h a s space R s. space 1 space l e f t space w i t h space h e r. space S o space space fraction numerator fraction numerator begin display style x over 2 end style minus 1 over denominator 2 end fraction minus 2 over denominator 2 end fraction minus 3 equals 1 S o l v i n g space t h i s space e q u a t i o n space g i v e s fraction numerator begin display style x over 2 end style minus 1 over denominator 2 end fraction minus 2 equals 8 x over 2 minus 1 equals 20 x equals 42 S o space s h e space s t a r t e d space w i t h space R s. space 42 space

Answered by Dharma Teja | 5th Jun, 2014, 11:19: AM