Question

Question 97

A lady buys some pencils for Rs.3 and equal number for Rs. 6. She sells them for Rs. 7. Find her gain of loss %

Answer 1

Let the Lady buys x number of pencils for Rs. 3.
Cost price for one pencil, $C{P}_1$ = Rs. $\frac{3}{x}$
Also, she buys same number of pencils for Rs. 6
$\therefore$ Cost price for one pencil, $C{P}_2$ = Rs $\frac{6}{x}$
Now, total pencils = x + x = 2x.
She sells, 2x pencils = Rs. 7
$\therefore$ Selling price of 1 pencil = Rs. $\frac{7}{2x}$
Case I We know that, Gain = SP - CP
$\therefore$ Gain = Rs. $(\frac{7}{2x}-\frac{3}{x})=Rs.\left(\frac{7-6}{2x}\right)=Rs.\frac{1}{2x}\therefore Gain\%=\frac{Gain}{CP}\times 100=\frac{\frac{1}{2x}}{\frac{3}{x}}\times 100=\frac{100}{2\times 3}=\frac{50\%}{3}$
Case II
Also, we know that,
Loss = CP - SP
Loss = $\frac{6}{x}-\frac{7}{2x}=\frac{6\times 2-7}{2x}=Rs.\frac{5}{2x}\therefore Loss\%=\frac{Loss}{CP}\times 100=\frac{\frac{5}{2x}}{\frac{6}{x}}\times 100=\frac{250}{6}=\frac{125}{3}\%\therefore NetLoss\%=\frac{125}{3}-\frac{50}{3}=\frac{75}{3}=25\%$