Ramesh purchased two mobile phones from a shop. He sold first mobile phone at the price of ₹ 18750 and the second mobile phone at the price of ₹ 14250. If the profit percent on first mobile phone is five times of the loss percent on the second mobile phone, then find out the overall profit made by Ramesh after selling both the mobile phones, given that he purchased both at same cost.

Let the C.P of one mobile phone be $$₹x$$. 

S.P of first mobile phone = ₹18,750

S.P of second mobile phone = ₹14,250

Let the loss percent, incurred on the second mobile phone be $$p\ \%$$. 

Profit percentage, incurred on the first mobile phone = $$\left(5\times p\%\right)=5p\ \%$$

Now, we will use the profit-and-loss percentage formula. 

For the first mobile phone: 

Profit percentage = $$\dfrac{\left(\text{S.P}\ -\ \text{C.P}\right)}{\text{C.P}}\times100$$

$$5p=\dfrac{\left(₹18,750-₹x\right)}{₹x}\times100$$                                        $$\longrightarrow\ i$$

For the second mobile phone: 

Loss percentage = $$\dfrac{\left(\text{C.P}\ -\ \text{S.P}\right)}{\text{C.P}}\times100$$

$$p=\dfrac{\left(₹x-₹14,250\right)}{₹x}\times100$$                                        $$\longrightarrow\ ii$$

From equations $$i$$ and $$ii$$, we have to find the value of $$x$$.

Divide equation $$i$$ by equation $$ii$$,

$$\dfrac{5p}{p}=\dfrac{\dfrac{\left(₹18,750-₹x\right)}{₹x}\times100}{\dfrac{\left(₹x-₹14,250\right)}{₹x}\times100}$$

$$5=\dfrac{\left(18,750-x\right)}{\left(x-14,250\right)}$$

$$5\left(x-14,250\right)=\left(18,750-x\right)$$

$$5x-\left(5\times14,250\right)=18,750-x$$

$$5x+x=18,750+\left(5\times14,250\right)$$

$$6x=18,750+71,250=90,000$$

$$x=15,000$$

Hence, the C.P of one mobile phone is ₹15,000.

Total S.P = ₹18,750 + ₹14,250 = ₹33,000

Total C.P = $$₹2x$$ = $$₹\left(2\times15,000\right)=₹30,000$$

Overall Profit = Total S.P - Total C.P = ₹33,000 - ₹30,000 = ₹3,000

Overall Profit percentage = $$\dfrac{₹3,000}{₹30,000}\times100=10\%$$

Hence, the overall profit percentage of the transaction is 10%.

$$\therefore$$ The required answer is D.