Cost of 4 pens, 6 notebooks and 9 files is Rs. 305. 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?
465
Let pen=p, notebook=n, file=f. Given:
\[4p+6n+9f=305 \quad (1)\]\[3p+4n+2f=145 \quad (2)\]
Step 1 — Find combination: Seek \(x,y\) with \(x(4p+6n+9f)+y(3p+4n+2f)=5p+8n+16f\). Matching coefficients: \(4x+3y=5,\ 6x+4y=8,\ 9x+2y=16\). Solving gives \(x=2,\ y=-1\) (check: \(4(2)+3(-1)=5\) ✓).
Step 2 — Compute cost:
\[2(305)-1(145)=610-145=465\]
Therefore the cost is Rs. 465.
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