Question

Find the SP when:

(i) CP = Rs 950, gain = 6%
(ii) CP = Rs 9600, gain = $16\frac{2}{3}\%$
(iii) CP = Rs 1540, loss = 4%
(iv) CP = Rs 8640, loss = $12\frac{1}{2}\%$

Answer 1

(i) CP = Rs. 950
Gain = 6%

$$\begin{gathered} SP\; =\{\frac{(100+G\mathrm{ain}\%)}{100}\times \mathrm{CP}\} \\ =\{\frac{(100+6)}{100}\times 950\} \\ =\frac{106}{100}\times 950 \\ =\frac{100700}{100} \\ =\mathrm{Rs}.1007 \end{gathered}$$


(ii) CP = Rs. 9600
Gain = $16\frac{2}{3}\%=\frac{50}{3}\%$

$$\begin{gathered} \mathrm{S}\mathrm{P}=\{\frac{(100+G\mathrm{ain}\%)}{100}\times \mathrm{CP}\} \\ =\{\frac{(100+{\displaystyle \frac{50}{3}})}{100}\times 9600\} \\ =\frac{350}{300}\times 9600 \\ =\frac{3360}{3} \\ =\mathrm{Rs}.11200 \end{gathered}$$


(iii) CP = Rs. 1540
Loss = 4%

$$\begin{gathered} \mathrm{S}\mathrm{P}=\{\frac{(100-L\mathrm{oss}\%)}{100}\times \mathrm{CP}\} \\ =\{\frac{(100-4)}{100}\times 1540\} \\ =\frac{96}{100}\times 1540 \\ =\frac{147840}{100} \\ =\mathrm{Rs}.1478.40 \end{gathered}$$


(iv) CP = Rs. 8640
Loss = $12\frac{1}{2}\%=\frac{25}{2}\%$

$$\begin{gathered} \mathrm{S}\mathrm{P}=\{\frac{(100-L\mathrm{oss}\%)}{100}\times \mathrm{CP}\} \\ =\{\frac{(100-{\displaystyle \frac{25}{2}})}{100}\times 8640\} \\ =\frac{175}{200}\times 8640 \\ =\frac{1512000}{200} \\ =\mathrm{Rs}.7560 \end{gathered}$$