Determine Original Costs of Pens and Pencils

Let the original cost of one pen be denoted by $p$ and the original cost of one pencil be denoted by $c$. We can set up a system of linear equations based on the information given.

Formulate Cost Equations

From the first statement, the cost of 2 pens and 15 pencils is ₹286:

$ 2p + 15c = 286 \quad (1) $

The second scenario involves changes in costs. The cost of a pen decreases by ₹4 (new cost $p-4$) and the cost of a pencil increases by ₹2 (new cost $c+2$). The cost of 17 pens and 3 pencils under these new conditions is ₹128:

$ 17(p - 4) + 3(c + 2) = 128 $

Simplify this equation:

$ 17p - 68 + 3c + 6 = 128 $

$ 17p + 3c - 62 = 128 $

$ 17p + 3c = 128 + 62 $

$ 17p + 3c = 190 \quad (2) $

Solve the System of Equations

We have the system:

1. $ 2p + 15c = 286 $
2. $ 17p + 3c = 190 $

To eliminate $c$, multiply equation (2) by 5:

$ 5 \times (17p + 3c) = 5 \times 190 $

$ 85p + 15c = 950 \quad (3) $

Subtract equation (1) from equation (3):

$ (85p + 15c) - (2p + 15c) = 950 - 286 $

$ 83p = 664 $

$ p = \frac{664}{83} $

$ p = 8 $

Substitute the value of $p=8$ into equation (1):

$ 2(8) + 15c = 286 $

$ 16 + 15c = 286 $

$ 15c = 286 - 16 $

$ 15c = 270 $

$ c = \frac{270}{15} $

$ c = 18 $

So, the original cost of a pen is ₹8 and the original cost of a pencil is ₹18.

Calculate the Final Required Cost

We need to find the original cost of 11 pens and 8 pencils:

Cost = $ 11p + 8c $

Cost = $ 11(8) + 8(18) $

Cost = $ 88 + 144 $

Cost = $ 232 $

The original cost of 11 pens and 8 pencils is ₹232.