Question

Rs 9000 were divided equally among a certain number of persons. had there been 20 more persons ,each would have got Rs 160 less.find the original number of persons.

Expert Reply
Vimala Ramamurthy
Tue April 21, 2015
L e t space x space b e space t h e space n u m b e r space o f space p e r s o n s. A s s u m i n g space t h a t comma space R s.9000 space h a s space b e e n space d i v i d e d space e q u a l l y space a m o n g space t h e space p e r s o n s comma e a c h space p e r s o n space g o t equals 9000 over x I f space t h e r e space w e r e space 20 space m o r e space p e r s o n s comma space t h e space a m o u n t space o f space m o n e y space e a c h space g o t equals fraction numerator 9000 over denominator x plus 20 end fraction G i v e n space t h a t space fraction numerator 9000 over denominator x plus 20 end fraction equals 9000 over x minus 160 rightwards double arrow 9000 over x minus fraction numerator 9000 over denominator x plus 20 end fraction equals 160 rightwards double arrow fraction numerator 9000 open parentheses x plus 20 close parentheses minus 9000 x over denominator x open parentheses x plus 20 close parentheses end fraction equals 160 rightwards double arrow fraction numerator 9000 x plus 180000 minus 9000 x over denominator x open parentheses x plus 20 close parentheses end fraction equals 160 rightwards double arrow fraction numerator 180000 over denominator x open parentheses x plus 20 close parentheses end fraction equals 160 rightwards double arrow 1125 equals x open parentheses x plus 20 close parentheses rightwards double arrow x squared plus 20 x minus 1125 equals 0 rightwards double arrow x squared plus 45 x minus 25 x minus 1125 equals 0 rightwards double arrow x open parentheses x plus 45 close parentheses minus 25 open parentheses x plus 45 close parentheses equals 0 rightwards double arrow open parentheses x plus 45 close parentheses open parentheses x minus 25 close parentheses equals 0 rightwards double arrow x plus 45 equals 0 space o r space x minus 25 equals 0 rightwards double arrow x equals negative 45 space o r space x equals 25 N u m b e r space o f space p e r s o n s space c a n n o t space b e space n e g a t i v e space a n d space h e n c e comma space x equals 25 T h u s comma space t h e space m o n e y space R s.9000 space h a s space b e e n space d i v i d e d space a m o n g space 25 space p e r s o n s.
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