Question : The cost of 4 pens, 6 notebooks, and 9 files is Rs. 305. The cost of 3 pens, 4 notebooks and 2 files is Rs. 145. What is the cost (in Rs.) of 5 pens, 8 notebooks, and 16 files?
Option 1: 515
Option 2: 565
Option 3: 540
Option 4: Can not be determined
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Correct Answer: 565
Solution :
Let the cost of 1 pen, 1 notebook and 1 file be Rs. $x, y$ and $z$, respectively.
The cost of 4 pens, 6 notebooks, and 9 files is Rs. 305.
The cost of 3 pens, 4 notebooks and 2 files is Rs. 145.
So, $4x + 6y+ 9z = 305$ (Equation1)
$3x + 4y + 2z = 145$ (Equation2)
Performing 2 × (Equation1) – (Equation2), we get
$5x + 8y + 16z = 2(305) - 145$
⇒ $5x + 8y + 16z = 565$
Hence, the correct answer is 565.
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