Question

Two types of boxes A, B are to be placed in a truck having capacity of 10 tons. When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons. But when 260 boxes of type A are loaded in the truck, it can still accommodate 40 boxes of type B, so that it is fully loaded. Find the weight of each type of box. Solve this word problem

Answer 1

let the of weight of each A types box = A

and the mass of each B types of box = B


according to question,


150 boxes of type A and 100 boxes of type B weighs =10 tons 

= 150A + 100B = 10

= 15A + 10B = 1--------( 1 )


Now,


260 boxes of type A and 40 boxes of type B 

weighs = 10 tons

= 260A + 40B = 10

= 26A + 4B = 1-----( 2 )



from--(1) and--(2)
multiply by 2 * --(1) and by 5 *--(2)


30A + 20B = 2
130A + 20B = 5
(-)____(-)____(-)
------------------------
-100A = -3

A = 3/100tons ( put in--(1) )



15(3/100) + 10B = 1

= 9/20 + 10B = 1


= (9 + 200B)/20 = 1

= 9 + 200B = 20

= 200B = 11

=> B = 11/200tons



weight of each A type of box = 3/100 × 1000kg

= 30kg


the weight of each B type of box = 11/200 × 1000kg

= 11×5 = 55kg

Answer 2

Let x be the weight of each A type box
and y be the weight of each B type box

A.T.Q -
1st case :
150 boxes of type A & 100 boxes of type B weighs =10 tons
150x + 100y = 10
15x + 10y = 1…………...( 1 )
[Divide by 10 both sides]

2nd case:
260 boxes of type A and 40 boxes of type B weighs = 10 tons
260x+ 40y = 10
26x + 4y = 1……………..(2)
[Divide by 10 both sides]

On multiplying eq (1) by 2 and eq 2 by 5 and subtract eq 4 from 3
30x + 20y = 2…………(3)
130x + 20y = 5……….(4)
(-) (-) (-)
------------------------
-100x = - 3

x = 3/100 tons
Weight of each A type box = 3/100 tons

On Putting x = 3/100 in eq 1,
15x + 10y = 1
15(3/100) + 10y = 1
9/20 + 10y = 1
(9 + 200y)/20 = 1
9 + 200y = 20
200y = 11
y= 11/200

Weight of each B type box = 11/200 tons

Hence, the weight of each A type of box = 3/100 × 1000 kg = 30kg
& the weight of each B type of box = 11/200 × 1000 kg= 11×5 = 55 kg
[ 1 ton = 1000 kg ]

HOPE THIS WILL HELP YOU...