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Q.

State True or False.


The cost of 2 kg of apples and 1 kg of grapes per day is Rs.160. After a month, 4 kg of apples and 2 kg of grapes cost Rs.300. The system of linear equations formed for this situation is parallel.


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a

True

b

False 

answer is A.

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Detailed Solution

Given that the cost of 2 kg of apples and 1 kg of grapes per day is Rs.160.
We know that for the given pair of linear equations to be parallel or inconsistent, the comparison of a 1 a 2 , b 1 b 2  and  c 1 c 2   must satisfy the condition a 1 a 2 = b 1 b 2 ≠ c 1 c 2 .  
Let the cost of 1kg apples = Rs. x,
And the cost of 1kg grapes = Rs. y.
Cost of 2kg of apples and 1kg of grapes = Rs. 160.
By representing the above statement in algebraic form,
2x+y=160   ⇒2x+y−160=0    ….  1  
After a month, the cost of 4kg of apples and 2kg of grapes = Rs. 300.
By representing the above statement in algebraic form,
4x+2y=300   ⇒4x+2y−300=0    ….  2  
Here,
a 1 =2, b 1 =1, c 1 =−160, a 2 =4, b 2 =2, c 2 =−300. a 1 a 2 = 2 4 ⇒ a 1 a 2 = 1 2 , b 1 b 2 = 1 2 , c 1 c 2 = −160 −300 ⇒ c 1 c 2 = 8 15  
Therefore,
a 1 a 2 = b 1 b 2 ≠ c 1 c 2 .  
The formed pair of linear equations, 2x + y = 160 and 4x + 2y = 300 are parallel.
Thus, the statement is true.
Hence,  the correct option is 1.
 
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