# Find the cost price when:

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) $\mathrm{SP}=$ Rs $34.40$ and gain $\%=7 \frac{1}{2} \%$

Solution:

(i) $\mathrm{SP}=$ Rs. 1596

Gain percentage $=12 \%$

$\mathrm{CP}=\frac{100}{(100+\text { gain } \%)} \times \mathrm{SP}$

$=\frac{100}{(100+12)} \times 1596$

$=$ Rs. 1425

(ii) $\mathrm{SP}=$ Rs. 2431

Loss percentage $=6 \frac{1}{2} \%=\frac{13}{2} \%$

$\mathrm{CP}=\frac{100}{(100-\text { loss } \%)} \times \mathrm{SP}$

$=\frac{100}{\left(100-\frac{13}{2}\right)} \times 2431$

$=\frac{100 \times 2}{187} \times 2431$

$=$ Rs. 2600

(iii) SP $=$ Rs. $657.60$

Loss percentage $=4 \%$

CP $=\frac{100}{(100-\text { loss } \%)} \times$ SP

$=\frac{100}{(100-4)} \times 657.60$

$=$ Rs. 685

(iv) $\mathrm{SP}=$ Rs. $34.40$

Gain percentage $=7 \frac{1}{2} \%=\frac{15}{2} \%$

$\mathrm{CP}=\frac{100}{(100+\text { gain } \%)} \times \mathrm{SP}$

$=\frac{100}{\left(100+\frac{15}{2}\right)} \times 34.40$

$=\frac{100 \times 2}{215} \times 34.40$

$=$ Rs. 32