Question

Find the gain or loss per cent when:
(i) CP = Rs 620 and SP = Rs 713
(ii) CP = Rs 675 and SP = Rs 630
(iii) CP = Rs 345 and SP = Rs 372.60
(iv) CP = Rs 80 and SP = Rs 76.80

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{CP}=\mathrm{Rs}.620 \\ \mathrm{SP}=\mathrm{Rs}.713 \\ \mathrm{Since}\mathrm{SP}>\mathrm{CP},\mathrm{there}\mathrm{is}\mathrm{a}\mathrm{gain}. \\ \mathrm{Gain}=713-620=\mathrm{Rs}.93 \\ \mathrm{Gain}\mathrm{percentage}=(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100)\% \\ =(\frac{93}{620}\times 100)\% \\ =15\% \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}675 \\ \mathrm{SP}=\mathrm{Rs}630 \\ \mathrm{Since}\mathrm{SP}<\mathrm{CP},\mathrm{there}\mathrm{is}\mathrm{a}\mathrm{loss}. \\ \mathrm{Loss}=675-630=\mathrm{Rs}.45 \\ \mathrm{Loss}\mathrm{percentage}=(\frac{\mathrm{Loss}}{\mathrm{CP}}\times 100)\% \\ =(\frac{45}{675}\times 100)\% \\ =6\frac{2}{3}\% \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}.345 \\ \mathrm{SP}=\mathrm{Rs}.372.60 \\ \mathrm{Since}\mathrm{SP}>\mathrm{CP},\mathrm{there}\mathrm{is}\mathrm{a}\mathrm{gain}. \\ \mathrm{Gain}=372.60-345=\mathrm{Rs}.27.6 \\ \mathrm{Gain}\mathrm{percentage}=(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100)\% \\ =(\frac{27.6}{345}\times 100)\% \\ =\left(\frac{2760}{345}\right)\% \\ =8\% \end{gathered}$$

(iv)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}80 \\ \mathrm{SP}=\mathrm{Rs}76.80 \\ \mathrm{Since}\mathrm{SP}<\mathrm{CP},\mathrm{there}\mathrm{is}\mathrm{a}\mathrm{loss}. \\ \mathrm{Loss}=80-76.80=\mathrm{Rs}.3.2 \\ \mathrm{Loss}\mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{CP}}\times 100)\% \\ =(\frac{3.2}{80}\times 100)\% \\ =(\frac{32}{80}\times 100)\% \\ =4\% \end{gathered}$$