Question

b) Mrs. Shakya sold a jewellery at a loss of 5%. If she had sold it at Rs 5,200 more,
she would have gained 8%. Find the cost price of the jewellery,​

Answer 1

Answer:

$\huge{ \fbox{ \sf{Rs \: 40000}}}$

Step-by-step explanation:

$\sf{Let \: CP \: ( \: cost \: price) \: be \: x}$

$\sf{Loss \: \% \: = 5 \% \: }$

$\sf{Selling \: price = CP \: - \: loss \: \% \: of \: CP}$

$\mapsto{ \sf x - \frac{5}{100} \times x}$

$\mapsto{ \sf{x - \frac{x}{20} }}$

$\mapsto{ \sf{ \frac{x \times 20 - x}{20} }}$

$\mapsto{ \sf{ \frac{20x - x}{20}}}$

$\mapsto{ \sf{ \frac{19x}{20}}}$

Now, Finding the New selling price

$\sf{New \: SP \: ( \: selling \: price)} = \frac{19x}{20} + 5200$

$\mapsto{ \sf{ \frac{19x + 5200 \times 20}{20}}}$

$\mapsto{ \sf{ \frac{19x + 10400}{20}}}$

Finally, finding the Cost price :

We have, Profit % = 8 %

$\sf{Cost \: price = Selling \: price \: - \: P\% \: of \: CP}$

$\mapsto{ \sf{x = \frac{19x + 104000}{20} - 8\% \: of \: x}}$

$\mapsto{ \sf{x = \frac{19x + 104000}{20} - \frac{8x}{100} }}$

$\mapsto{ \sf{x = \frac{19x + 104000}{20} - \frac{2x}{25} }}$

$\mapsto{ \sf{x = \frac{5(19x + 104000) - 2x \times 4}{100} }}$

$\mapsto{ \sf{x = \frac{95x + 520000 - 8x}{100} }}$

$\mapsto{ \sf{x = \frac{87x + 520000}{100}}}$

$\mapsto{ \sf{100x = 87x + 520000}} \: \: ( \sf{Cross \: multiplication}$

$\mapsto{ \sf{100x - 87x = 520000}}$

$\mapsto{ \sf{13x = 520000}}$

$\mapsto{ \sf{x = \frac{520000}{13}}}$

$\mapsto{ \boxed {\sf{x = 40000}}}$

Therefore, the cost price of the jewellery is Rs 40000

Hope I helped!

Best regards! :D

~$\sf{TheAnimeGirl}$