Question
Sun March 22, 2015 By: Manisha Behera

A trust caring for handicapped children gets Rs. 30,000 every month from its donors. the trust spends half of the funds received for medical and educational care of the children and for that it charges 2% of the spent amount from them, and deposits the balance amount in a private bank to get the money multiplied so that in future the trust goes on functioning regularly. What percent of interest should the trust get from the bank to get a total of Rs. 1800 every month ?

solve this using matrices

Expert Reply
satyajit samal
Mon March 23, 2015
O u t space o f space 30 comma 000 space r u p e e s space r e c e i v e d comma space t h e space t r u s t space s p e n d s space h a l f space f o r space m e d i c a l space a n d space e d u c a t i o n space c a r e. space H e n c e comma space t h e space a m o u n t space d e p o s i t e d space i n space p r i v a t e space b a n k space i s space t h e space r e m a i n i n g space h a l f space equals space 15 comma 000 space r u p e e s. space T h e space t r u s t space c h a r g e s space 2 % space o f space t h e space m o n e y space s p e n t space f o r space m e d i c a l space a n d space e d u c a t i o n a l space c a r e. space H e n c e comma space t h e space e a r n i n g space o f space t h e space t r u s t space f r o m space t h e space a b o v e space c h a r g e s space i s space 2 % space o f space 15 comma 000 space equals space 15 comma 000 space asterisk times space 2 divided by 100 space equals space 300 space r u p e e s. L e t space t h e space e a r n i n g space o f space t h e space t r u s t space f r o m space t h e space a b o v e space c h a r g e s space b e space apostrophe X apostrophe space a n d space t h e space e a r n i n g space f r o m space i n t e r e s t space o b t a i n e d space f r o m space t h e space b a n k space b e space apostrophe Y apostrophe W e space h a v e space t h e space f o l l o w i n g space s y s t e m space o f space e q u a t i o n s colon X plus Y equals 1800 semicolon X equals 300 T h e space a b o v e space t w o space e q u a t i o n s space c a n space b e space w r i t t e n space i n space m a t r i x space f o r m space a s space open square brackets table row 1 1 row 1 0 end table close square brackets open square brackets table row X row Y end table close square brackets equals open square brackets table row 1800 row 300 end table close square brackets rightwards double arrow open square brackets table row X row Y end table close square brackets equals open square brackets table row 1 1 row 1 0 end table close square brackets to the power of negative 1 end exponent open square brackets table row 1800 row 300 end table close square brackets rightwards double arrow open square brackets table row X row Y end table close square brackets equals fraction numerator open square brackets table row 0 cell negative 1 end cell row cell negative 1 end cell 1 end table close square brackets over denominator negative 1 end fraction open square brackets table row 1800 row 300 end table close square brackets rightwards double arrow open square brackets table row X row Y end table close square brackets equals open square brackets table row 0 1 row 1 cell negative 1 end cell end table close square brackets open square brackets table row 1800 row 300 end table close square brackets rightwards double arrow open square brackets table row X row Y end table close square brackets equals open square brackets table row 300 row 1500 end table close square brackets H e n c e comma space w e space g e t space Y equals 1500. L e t space t h e space m o n t h l y space i n t e r e s t space r a t e space b e space R %. space H e n c e space R % space o f space 15 comma 000 equals space 1500 rightwards double arrow R over 100 cross times 15 comma 000 equals 1500 rightwards double arrow R equals 10 %
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