Question

Find the cost price when:
(i) SP = Rs 1596 and gain% = 12%
(ii) SP = Rs 2431 and loss% = $6\frac{1}{2}\%$
(iii) SP = Rs 657.60 and loss% = 4%
(iv) SP = Rs 34.40 and gain% = $7\frac{1}{2}\%$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{SP}=\mathrm{Rs}.1596 \\ \mathrm{Gain}\mathrm{percentage}=12\% \\ \mathrm{CP}=\frac{100}{(100+\mathrm{gain}\%)}\times \mathrm{SP} \\ =\frac{100}{(100+12)}\times 1596 \\ =\mathrm{Rs}.1425 \end{gathered}$$

(ii)

$$\begin{gathered} \mathrm{SP}=\mathrm{Rs}.2431 \\ \mathrm{Loss}\mathrm{percentage}=6\frac{1}{2}\%=\frac{13}{2}\% \\ \mathrm{CP}=\frac{100}{(100-\mathrm{loss}\%)}\times \mathrm{SP} \\ =\frac{100}{(100-{\displaystyle \frac{13}{2}})}\times 2431 \\ =\frac{100\times 2}{187}\times 2431 \\ =\mathrm{Rs}.2600 \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{SP}=\mathrm{Rs}.657.60 \\ \mathrm{Loss}\mathrm{percentage}=4\% \\ \mathrm{CP}=\frac{100}{(100-\mathrm{loss}\%)}\times \mathrm{SP} \\ =\frac{100}{(100-4)}\times 657.60 \\ =\mathrm{Rs}.685 \end{gathered}$$

(iv)
$$\begin{gathered} \mathrm{SP}=\mathrm{Rs}.34.40 \\ \mathrm{Gain}\mathrm{percentage}=7\frac{1}{2}\%=\frac{15}{2}\% \\ \mathrm{CP}=\frac{100}{(100+\mathrm{gain}\%)}\times \mathrm{SP} \\ =\frac{100}{(100+{\displaystyle \frac{15}{2}})}\times 34.40 \\ =\frac{100\times 2}{215}\times 34.40 \\ =\mathrm{Rs}.32 \end{gathered}$$