two type of boxes A and B are to be placed in a truck having capacity of 10 tones when 150 boxes of type a and hundred boxes of type B are loaded in the truck it weight 10 tones 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 boxes
Answers
Answer:
150A+115B=10 tonnes . Multiply this by 2.
300A+230B=20 tonnes
.
300A+30B=10 tonnes , Subtract this from above
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200B=10 tonnes
B=10tonnes/200
B=1/20 tonne
.
150A+115B=10 tonnes
150A+115(1/20 tonne)=10 tonnes
150A+115/20 tonnes=10 tonnes
150A=200/20 tonnes-115/20 tonnes
150A=85/20 tonnes
A=85/3000 tonnes
A=17/600 tonnes
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ANSWER: Box A weighs 17/600 tonne; Box B weighs 1/20 tonne
.
CHECK:
300A+30B=10 tonnes
300(17/600)+30(1/20)=10 tonnes
(17/2)+(3/2)=10 tonnes
20/2 tonnes=10 tonnes
10 tonnes=10 tonnes
Step-by-step explanation:
⊕ANSWER⊕
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