How much does the pen weigh?

Question

Pawan is playing around with a two-plate scale and finds that the scale stays in equilibrium if one plate is filled with two keys, two coins and three toy soldiers OR one apple, one toy soldier and one lemon, and the other plate with a weight of 100 grams. One coin, one key, one soldier and one plum together weigh 50 grams. The lemon, the apple and the plum weigh exactly the same as one coin, one key, one soldier and one pen.
How much does the pen weigh?

Answer 1

(1) 2keys+2coins+3toy=100g
=> [2(1key+1coin+1toy)+1toy]=100g.........................................................................................(i)
(2) 1apple+1toy+1 lemon=100g
=> (1 apple+1 lemon)=(100-1 toy)............................................................................................(ii)
(3) (1coin+1 key+1 toy)+1 plum=50g
=> 1 plum=[50-(1 coin+1 key+1 toy)]........................................................................................(iii)
(4) (1 lemon+1 apple)+1 plum=(1coin+1key+1 toy)+1 pen.................................................(iv)
=> (100-1 toy)+[50-(1coin+1 key+1 toy)]=(1coin+1key)+1toy)+1pen...put the values of (ii)&(iii) in (iv)
=>1 toy={150-pen-[2(1coin+1key+1toy)]}................................................................................(v)
Now ,put values of (v) in to (i)
=>[2(1key+1coin+1toy)]+{150-pen-[2(1coin+1key+1toy)]}=100
=>150-pen=100
=>pen=50g
Ans :Weight of pen is 50grams