Question

By selling a pair of earrings at a discount of 25% on the marked price, a jeweler makes a profit of 16%. If the profit is ₹96, what is the cost price? What is the marked price and the price at which the pair was eventually bought?​

Answer 1

Step-by-step explanation:

Given,

Earrings are bought at 25% discount

Profit percent of seller = 16%

Gain = Rs 48

So, by using the formula,

Gain% = (gain/CP) × 100

16 = (48/CP) × 100

16/100 = 48/CP

CP = (48×100)/16

= Rs 300

Now, CP = Rs 300 Cost price of the earrings = Rs 300 Profit = Rs 48 Profit = SP – CP SP = Profit + CP = 48 + 300 = 348 Given, additional discount of 25% By using the formula MP = (100 × SP) / (100 – Discount %) = (100 × 348) / (100 – 25) = (100 × 348) / 75 = 34800/75 = Rs 464

∴ Marked Price is Rs 464, CP is 300 and Final selling price is 348.

Answer 2

$\huge\sf{\bold{\underline{Given:}}}$

• $\small\sf{Earrings\: are\: bought\: =\: 25\:\%\: discount}$
• $\small\sf{Profit\: percent\: of\: seller\: = \:16\:\%}$
• $\small\sf{Gain \:=\: Rs. \:48}$

${ }$

$\huge\sf{\bold{\underline{Find:}}}$

• $\small\sf{Cost\:Price\:=\:?}$
• $\small\sf{Marked\:Price\:=\:?}$
• $\small\sf{Final\:Selling\:Price\:=\:?}$

${ }$

$\huge\sf{\bold{\underline{Solution:}}}$

$\small\sf{\dag{\blue{\underbrace{By\:Using\:the\:formula:}}}}$

• $\small\sf{Gain\:\% \:=\:{\small{\sf{\frac{ gain}{CP}}}}}\:\small\sf{ \times \:100}$

$\small\sf{\:\rightarrow\:\: 16 \:=}\:\small\sf{\frac{48}{CP}}\:\small\sf{ \times \:100}$

$\small\sf{\:\rightarrow}\:\:\small\sf{\frac{ 16}{100}}\:\small\sf{ = }\:\small\sf{\frac{48}{CP}}$

$\small\sf{CP\: = }\:\small\sf{\frac{(48\:\times\:100)}{16}}$

$\small\sf{\:\rightarrow \:\:Rs. \:300}$

• $\small\sf{\bold{CP \:= \:Rs.\: 300}}$

━━━━━━━━━━━━━━━━━━━━━━━━━

$\small\sf{\bold{Now,}}$

$\small\sf{Cost\: price\: of \:the\: earrings \:=\: Rs.\:300}$

$\small\sf{Profit \:=\: Rs. \:48}$

$\small\sf{\dag{\blue{\underbrace{By\:Using\:the\:formula:}}}}$

• $\small\sf{\bold{Profit\: =\: SP \:– \:CP}}$
• $\small\sf{\bold{SP \:=\: Profit\: + \:CP}}$

$\small\sf{\:\rightarrow \:\:48 \:+ \:300}$

$\small\sf{\:\rightarrow\:\: 348}$

• $\small\sf{\bold{SP\:=\: Rs.\:348}}$

━━━━━━━━━━━━━━━━━━━━━━━━━

$\small\sf{⚘ \:Given,\: additional \:discount\: of \:25\:\%}$

$\small\sf{\dag{\blue{\underbrace{By\:Using\:the\:formula:}}}}$

• $\small\sf{MP\: = }\:\small\sf{\frac{(100 \:\times\: SP) }{(100\: – \:Discount \:\%)}}$

$\small\sf{\:\rightarrow}\:\:\small\sf{\frac{ (100\:\times \: 348) }{(100 \: - \:25)}}$

$\small\sf{\:\rightarrow}\:\:\small\sf{\frac{ (100\: \times \:348) }{75}}$

$\small\sf{\:\rightarrow }\:\:\small\sf{\frac{34800}{75}}$

$\small\sf{\:\rightarrow\:\: Rs. \:464}$

• $\small\sf{\bold{MP\:=\:Rs.\: 464}}$

━━━━━━━━━━━━━━━━━━━━━━━━━

$\small\sf{\underline{\underline{\pink{\bold{So,\:the\:Answers\:are\:-}}}}}$

• $\small\sf\purple{\bold{Marked \:Price\: \leadsto \:\red{Rs.\: 464}}}$
• $\small\sf\purple{\bold{Cost\:Price\: \leadsto \:\red{Rs.\:300 }}}$
• $\small\sf\purple{\bold{Final \:selling \:price\: \leadsto \:\red{Rs.\:348.}}}$

${\:\:\:\:\:\:\:\:\:────┈┈┈┄┄╌╌╌╌┄┄┈┈┈────}$$\small\sf{\color{green}{@ItsNothing}}$