Question

two types of boxes a and b are to be placed in a truck having capacity of of 10 tons when 150 boxes of type a and 100 boxes of type b are loaded in the truck it weighs 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

Answer 1

Let the weight of box 'a' = x kg
And the weight of box 'b' = y kg

A/C to question,
150 boxes of type 'a' and 100 boxes of type 'b' are loaded in the truck and it weighs 10tons.
∴ 150x + 100y = 10 × 1000 [ ∵1 tone = 1000 Kg ]
⇒150x + 100y = 10000
⇒3x + 2y = 200 -------(1)

Again, A/C to question, 260 boxes of type 'a' and 40 boxes of type 'b' are loaded and it weighs completely 10tons.
∴ 260x + 40y = 10000
⇒13x + 2y = 500 --------(2)

Solve equations (1) and (2),
Subtracting equation (1) from equation (2)
(13x + 2y) - (3x + 2y) = 500 - 200
⇒10x = 300
⇒x = 30 , put it in equation (1)
2y = 200 - 3 × 30 = 200 - 90 = 110
⇒y = 55

Hence , weight of box 'a' = 30 Kg
weight of box 'b' = 55Kg

Answer 2

Hi ,

Let us assume ,

weight of each A type box = x tons

weight of each B type box = y tons

according to the problem given ,

150 boxes of type A and 10 boxes of type

B weighs = 10 tons

150x + 100y = 10

15x + 10y = 1 ---( 1 )

260 boxes of type A and 40 boxes of

type B weighs = 10tons

260x + 40 y = 10

26x + 4y = 1 ---( 2 )

multiply equation ( 1 ) with 2 and equation

( 2 ) with 5 , we get

30x + 20y = 2 ---( 3 )

130x + 20y = 5 --( 4 )

subtract equation ( 3 ) from equation ( 4 )

we get

x = 3/100

put x in equation ( 3 ). we get

y = 11/200 tons

Therefore ,

weight of each type a box = x = 3/100 tons

x = ( 3/100 ) × 1000 kg

x = 30 kg

weight of each type B box = y = 11/200tons

y = ( 11/200 ) × 1000 kg

= 55 kg

I hope this helps you.

: )