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

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

Explanation:

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

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

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

`\mapsto{ \sf x - (5)/(100) * x}`

`\mapsto{ \sf{x - (x)/(20) }}`

`\mapsto{ \sf{ (x * 20 - x)/(20) }}`

`\mapsto{ \sf{ (20x - x)/(20)}}`

`\mapsto{ \sf{ (19x)/(20)}}`

Now, Finding the New selling price

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

`\mapsto{ \sf{ (19x + 5200 * 20)/(20)}}`

`\mapsto{ \sf{ (19x + 10400)/(20)}}`

Finally, finding the Cost price :

We have, Profit % = 8 %

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

`\mapsto{ \sf{x = (19x + 104000)/(20) - 8\% \: of \: x}}`

`\mapsto{ \sf{x = (19x + 104000)/(20) - (8x)/(100) }}`

`\mapsto{ \sf{x = (19x + 104000)/(20) - (2x)/(25) }}`

`\mapsto{ \sf{x = (5(19x + 104000) - 2x * 4)/(100) }}`

`\mapsto{ \sf{x = (95x + 520000 - 8x)/(100) }}`

`\mapsto{ \sf{x = (87x + 520000)/(100)}}`

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

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

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

`\mapsto{ \sf{x = (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}`