Question

Find the selling price when:
(i) CP = Rs 1650 and gain% = 4%
(ii) CP = Rs 915 and gain% = $6\frac{2}{3}\%$
(iii) CP = Rs 875 and loss% = 12%
(iv) CP = Rs 645 and loss% = $13\frac{1}{3}\%$

Answer 1

(i)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}.1650 \\ \mathrm{Gain}\mathrm{percentage}=4\% \\ \mathrm{SP}=\frac{(100+\mathrm{gain}\%)}{100}\times \mathrm{CP} \\ =\frac{(100+4)}{100}\times 1650 \\ =\frac{104\times 1650}{100} \\ =\mathrm{Rs}.1716 \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}.915 \\ \mathrm{Gain}\mathrm{percentage}=6\frac{2}{3}\%=\frac{20}{3}\% \\ \mathrm{SP}=\frac{(100+\mathrm{gain}\%)}{100}\times \mathrm{CP} \\ =\frac{(100+{\displaystyle \frac{20}{3}})}{100}\times 915 \\ =\frac{\left({\displaystyle \frac{320}{3}}\right)}{100}\times 915 \\ =\left(\frac{320}{3}\right)\times \left(\frac{1}{100}\right)\times 915 \\ =\mathrm{Rs}.976 \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}.875 \\ \mathrm{Loss}\mathrm{percentage}=12\% \\ \mathrm{SP}=\frac{(100-\mathrm{loss}\%)}{100}\times \mathrm{CP} \\ =\frac{(100-12)}{100}\times 875 \\ =\frac{77000}{100} \\ =\mathrm{Rs}.770 \end{gathered}$$

(iv)

$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}.645 \\ \mathrm{Loss}\mathrm{percentage}=13\frac{1}{3}\%=\frac{40}{3}\% \\ \mathrm{SP}=\frac{(100-\mathrm{loss}\%)}{100}\times \mathrm{CP} \\ =\frac{(100-{\displaystyle \frac{40}{3}})}{100}\times 645 \\ =\frac{\left({\displaystyle \frac{300-40}{3}}\right)}{100}\times 645 \\ =\left(\frac{260}{3}\right)\times \left(\frac{1}{100}\right)\times 645 \\ =\mathrm{Rs}.559 \end{gathered}$$