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Home / Doubts and Solutions/MAHARASHTRA OLD/Class 9/Mathematics

Solve the following using two variables:
A passenger is allowed some free luggage by Rajdhani Express. Two passengers have total 100kg luggage. They have to pay Rs.12 and Rs.8 as the luggage charges respectively. If one passenger was having the same luggage, he would have to pay Rs.30. Find how much free luggage each passenger is allowed to carry.

Asked by kishor.123 11th January 2015, 2:12 PM
Answered by Expert
Answer:
L e t space x space b e space t h e space f r e e space l u g g a g e space a l l o w e d space i n space R a j d h a n i space E x p r e s s. L e t space a space a n d space b space b e space t h e space l u g g a g e s space o f space t w o space p a s s e n g e r s. L e t space y space b e space t h e space cos t space p e r space k g space f o r space e x t r a space l u g g a g e. F r o m space t h e space g i v e n space s t a t e m e n t space o f space t h e space p r o b l e m comma space w e space h a v e comma space a plus b equals 100 space k g... left parenthesis 1 right parenthesis E x t r a space l u g g a g e space o f space f i r s t space p a s s e n g e r equals a minus x C o s t space f o r space f i r s t space p a s s e n g e r equals open parentheses a minus x close parentheses y equals R s.12... left parenthesis 2 right parenthesis E x t r a space l u g g a g e space o f space s e c o n d space p a s s e n g e r equals b minus x C o s t space f o r space s e c o n d space p a s s e n g e r equals open parentheses b minus x close parentheses y equals R s.8... left parenthesis 3 right parenthesis I f space o n e space p a s s e n g e r space h a d space 100 space k g comma space t h e n space e x c e s s space l u g g a g e equals 100 minus x T o t a l space cos t space f o r space e x t r a space l u g g a g e equals open parentheses 100 minus x close parentheses y A l s o space g i v e n space t h a t space t h e space cos t space f o r space a space sin g l e space p a s s e n g e r space w h o s e space l u g g a g e space i s space 100 minus x space i s space R s.30. therefore open parentheses 100 minus x close parentheses y equals R s.30 rightwards double arrow 100 y minus x y equals 30... left parenthesis 4 right parenthesis A d d e i n g space e q u a t i o n s space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space h a v e comma open parentheses a minus x close parentheses y plus open parentheses b minus x close parentheses y equals 12 plus 8 rightwards double arrow open parentheses a plus b close parentheses y minus 2 x y equals 20 rightwards double arrow 100 y minus 2 x y equals 20... left parenthesis 5 right parenthesis E q u a t i n g space r e q u a t i o n s space left parenthesis 4 right parenthesis space a n d space left parenthesis 5 right parenthesis comma space w e space h a v e comma x y plus 30 equals 2 x y plus 20 rightwards double arrow x y equals 10... left parenthesis 6 right parenthesis S u b s t i u t i n g space t h e space v a l u e space o f space x y space f r o m space e q a u a t i o n space left parenthesis 6 right parenthesis space i n space e q u a t i o n space left parenthesis 5 right parenthesis comma space w e space h a v e comma 100 y minus 2 cross times 10 equals 20 rightwards double arrow 100 y equals 20 plus 20 rightwards double arrow 100 y equals 40 rightwards double arrow y equals 40 over 100 equals R e.0.4 space p e r space k g S u b s t i t u t i n g space t h e space v a l u e space o f space y space i n space e q u a t i o n space left parenthesis 6 right parenthesis comma space w e space h a v e comma x y equals 10 rightwards double arrow x cross times 0.4 equals 10 rightwards double arrow x equals fraction numerator 10 over denominator 0.4 end fraction rightwards double arrow x equals 25 space k g S u b s t i t u t i n g space t h e space v a l u e space o f space x space a n d space y space i n space e q u a t i o n space left parenthesis 2 right parenthesis comma space w e space h a v e comma open parentheses a minus x close parentheses y equals R s.12 rightwards double arrow open parentheses a minus 25 close parentheses cross times 0.4 equals R s.12 rightwards double arrow open parentheses a minus 25 close parentheses equals fraction numerator 12 over denominator 0.4 end fraction rightwards double arrow a minus 25 equals 30 rightwards double arrow a equals 30 plus 25 rightwards double arrow a equals 55 space k g S i n c e space a plus b equals 100 comma space w e space h a v e comma space 55 plus b equals 100 rightwards double arrow b equals 100 minus 55 rightwards double arrow b equals 45 space k g
Answered by Expert 11th January 2015, 5:44 PM
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