The ratio of the cost price of a pen to that of a pencil is $3:4$. A shopkeeper marks up the price of both the pen and the pencil by $20\%$ above their respective cost prices. He then offers a $10\%$ discount on each item. If the shopkeeper's total profit from selling one pen and one pencil is Rs. $2.8$, what is the cost price of the pen?

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**Solution:**

1. Let the cost price of the pen be $3x$ and the cost price of the pencil be $4x$ (given ratio $3:4$).

2. The marked price (MP) of the pen is $20\%$ above cost price:
   $$	ext{MP of pen} = 3x + 0.20 	imes 3x = 3x 	imes 1.20 = 3.6x$$

3. Similarly, the marked price of the pencil is:
   $$	ext{MP of pencil} = 4x + 0.20 	imes 4x = 4x 	imes 1.20 = 4.8x$$

4. The shopkeeper gives a $10\%$ discount on each item, so the selling price (SP) of the pen is:
   $$	ext{SP of pen} = 3.6x - 0.10 	imes 3.6x = 3.6x 	imes 0.90 = 3.24x$$

5. The selling price of the pencil is:
   $$	ext{SP of pencil} = 4.8x - 0.10 	imes 4.8x = 4.8x 	imes 0.90 = 4.32x$$

6. Total cost price of pen and pencil:
   $$3x + 4x = 7x$$

7. Total selling price of pen and pencil:
   $$3.24x + 4.32x = 7.56x$$

8. Profit earned on selling both is Rs. $2.8$, so:
   $$	ext{Profit} = 	ext{SP} - 	ext{CP} = 7.56x - 7x = 0.56x = 2.8$$

9. Solve for $x$:
   $$x = \frac{2.8}{0.56} = 5$$

10. Cost price of the pen is:
    $$3x = 3 	imes 5 = 15$$

**Answer:** Rs. $15$

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