Moli buys 3 ribbons,7 clips and 1 soap for Rs.120 exactly. At the same place it would cost Rs.164 for 4 ribbons, 10 clips and one soap. How much would it cost for one ribbon, one clip and one soap ? Choose the correct choice.
A) 36 B) 34 C) 38 D) 32 E) 31

Rationale: explanation : let us consider , ribbon is denoted by r clips is denoted by c soaps is denoted by s now according to the question , = > 3 r + 7 c + s = 120 - - - - - - - - ( 1 ) = > 4 r + 10 c + s = 164 - - - - - - - - ( 2 ) ( 1 ) - ( 2 ) = > ( 3 r - 4 r ) + ( 7 c - 10 c ) + ( s - s ) = 120 - 164 = > - r - 3 c = - 44 multily the equation by - 1 , it becomes = > r + 3 c = 44 - - - - - - - ( 3 ) now perform this operation 2 * ( 1 ) - ( 2 ) = > 2 r + 4 c + s = 76 - - - - - - - ( 4 ) finaly ( 4 ) - ( 3 ) = > r + c + s = 32 hence , the cost of 1 ribbon , 1 clip and 1 saop would be 32 rs . answer : d
Answer: D