The ratio of cost price of a pen to that of a pencil is 3:4 and shopkeeper marked each of pen and pencil 20% above their respective cost prices. If shopkeeper allowed 10% discount on each of pen & pencil and earned a total of Rs. 2.8 on selling a pen & a pencil, then find the cost price of a pen.

The correct option is Rs.15.

Step-by-step Explanation:

Step 1: Define the Cost Prices

Let the cost price of a pen be CP_pen and the cost price of a pencil be CP_pencil.

According to the given ratio (3:4), we can assume:

${\mathrm{CP}}_{\mathrm{pen}}=3x$

${\mathrm{CP}}_{\mathrm{pencil}}=4x$

Step 2: Calculate Marked Prices

The shopkeeper marks each item 20% above its cost price.

Marked Price of the pen (MP_pen):

${\mathrm{MP}}_{\mathrm{pen}}=3x\×1.20=3.6x$

Marked Price of the pencil (MP_pencil):

${\mathrm{MP}}_{\mathrm{pencil}}=4x\×1.20=4.8x$

Step 3: Calculate Selling Prices

A discount of 10% is allowed on each item, meaning the selling price is 90% (or 0.9) of the marked price.

Selling Price of the pen (SP_pen):

${\mathrm{SP}}_{\mathrm{pen}}=3.6x\×0.9=3.24x$

Selling Price of the pencil (SP_pencil):

${\mathrm{SP}}_{\mathrm{pencil}}=4.8x\×0.9=4.32x$

Step 4: Calculate Total Profit and Find 'x'

Profit on an item is given by Profit = Selling Price - Cost Price.

Profit on pen = $3.24x-3x=0.24x$

Profit on pencil = $4.32x-4x=0.32x$

Total profit on selling one pen and one pencil:

$\text{Total Profit}=0.24x+0.32x=0.56x$

We are given that the total profit is Rs. 2.8:

$0.56x=2.8$

$x=\frac{2.8}{0.56}=5$

Step 5: Find the Cost Price of the Pen

The cost price of a pen is $3x$:

${\mathrm{CP}}_{\mathrm{pen}}=3\×5=\text{Rs.15}$