Question

two types of boxes a,b are to be place 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 , itcan still accommodate 40 boxes of type b , so that it is fully loaded . find the weight of each type of box

Answer 1

Solution:

ATQ, 150A+100B= 10 tons.
=>15A+10B= 1.....(1)

Now according to second condition,

=>260A+ 40 B= 10

=> 26A+ 4B= 1....(2)

solving 1 &2 by elimination method.

multiply 1 with 2 and 2 with 5. we get.

=>30A+20B= 2.....(3)
=>130A+ 20B= 5.....(4)

Now,subtract 3 from 4.

=>-100A= -3

=> A= 3/100 tones.

putting the value of A. in 1

=> 15*3/100+4B= 1
=> 9/20+4B=1
=> (9+80B)/20=1
=> 9+80B=20
=> 80B= 11
=> B= 11/80

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Answer 2

Heya

Let the weight of box a be 'a' and box b be 'b'

150a + 100b make up 10 tonnes....(1)

The truck is fully loaded when it has 10 tonnes in it.

260a + 40b = 10 tonnes....(2)

2×(1) - 5(2)

300a+200b=20
-1300a-200b=-50

=> -1000a= -30

a = -30/-1000 = 0.03tonnes.

Substituting the value of a in equation 1

150a+100b= 10

150(0.03) + 100b = 10

4.5 + 100b = 10

b = 5.5/100 = 0.055 tonnes.

Hope it helps!