1) By selling a pen for Rs.165. Mukti gains 10%. she had sold it for Rs.157.50 What percenatge would she have lost or gained? 2) By selling a watch for Rs 1275 .Javed lost 15%. At what price should he sell and make a profit of 10%

Q-1
Suppose the cost price of  pen is x.
Now for gain = 10%, we have;
selling price = $x+x\times \frac{10}{100} = \frac{11x}{10}$ = Rs.165
$$\begin{gathered} \Rightarrow 11x = 165\times 10 \\ \Rightarrow x = \frac{165\times 10}{11} = 150 \end{gathered}$$
so cost price of pen = Rs.150
Now when she sold at Rs.157.50.
Then net gain = Rs.157.50 - Rs.150 = Rs.7.50
Therefore gain percentage = $\frac{\mathrm{net} \mathrm{gain}\times 100}{\mathrm{cost} \mathrm{price}} = \frac{7.50\times 100}{150}$ = 5%

Q-2
$$\begin{gathered} Let the \cos t price be x \\ SP = 1275Rs \\ Loss = CP-SP \\ Loss\% =\frac{(CP-SP)}{CP}\times 100 \\ Loss\% = 15 \\ 15 = \frac{x-1275}{x}\times 100 \\ 15x =100x -127500 \\ or 85x =127500 \\ x=1500 Rs. \\ So the CP is 1500Rs. \\ Second case : profit of 10\% \\ so Profit = SP\hspace{0.17em}-CP \\ let SP = y, CP\hspace{0.17em}= 1500Rs \\ Profit\% =\frac{SP-CP}{CP}\times 100 \\ 10 = \frac{y-1500}{1500}\times 100 \\ 10 =\frac{y-1500}{15} , 150 =y -1500 , y =1500+150 =1650Rs So the selling price is 1650Rs. \end{gathered}$$