Question

Two types of boxes A, B are to be placed in a truck having a capacity 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 weight of 1 box A = a

Let weight of 1 box B = b

So, we have

150a + 100b = 10000      [10 tons = 10000kgs]

or 3a + 2b = 200......(1)

And, 260a + 40b = 10000

or 13a + 2b = 500....(2)

solving (1) and (2), we get

10a = 300

a = 30 kg

So, 3(30) + 2b = 200

90 + 2b = 200

2b = 110

b = 55 kg

Therefore weights of boxes are 30 kg and 55 kg.

Answer 2

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