Question

the shopkeeper gain 7% by selling an article for 3852Rs. If he sell it for 4050Rs,find the gain percent?
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Answer 1

$\large\boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \green{Question}} \purple{\mid} }} } : - \:$

The shopkeeper gains 7% by selling an article for Rs. 3852 . If he sell it for Rs. 4050 .find the gain percent?

$\large\boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \red{Answer}} \purple{\mid} }} } : - \: \\ \\ \to \green{\boxed{\sf \red{x = 12.5}\%}} \: \\ \\ \large \boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \pink{To \: Find}} \purple{\mid} }} } : - \: \\ \implies \sf \: Gain \: percentage \\ \\ \large \boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \green{Explanation}} \purple{\mid} }} } : - \:$

$\pink{\bf{Given}\begin{cases}\sf{ \red{Selling \: price (s) = }Rs. 3822 \: }\\\sf{ \green{Gain \: \% = 7}\% \: }\\ \sf{S' \: \blue{ =Rs. \: 4050}}\end{cases}}</p><p> \:$

Let , S → Selling price , C → Cost price and s' be the another selling price

$\large\boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \green{Solution}} \purple{\mid} }} } : - \:$

We know that :

$\boxed{ \sf \red{Gain \: \% = } \frac{selling \: price - cost \: price}{cost \: price} \times 100}$

substitute the given values -

$\mapsto \sf \red{7 = } \green{ \frac{3852 - c}{c}} \times 100 \\ \\ \mapsto \sf \pink{ 7 \: c =} 385200 \blue{ - 100 \: c \: } \\ \\ \mapsto \sf \green{ 107 \: c =} 385200 \\ \\ \mapsto \boxed{ \sf \: c = \frac{385200}{107}}$

When selling price (s') is Rs. 4050 ,let gain is "x"

$\to \sf x = \frac{ \blue{4050 - c}}{c} \times \pink{ 100} \\ \\ \to \sf \: x = \frac{ \red{4050 - \frac{385200}{107}} }{ \green{ \frac{385200}{107} }} \times 100 \\ \\ \to \sf x = \frac{ \purple{4050 \times 107 -} 385200}{ \red{3852}} \\ \: \\ \to \sf x = \frac{ \red{433350 - 385200}}{ \pink{3852}} \\ \\ \to \sf \: x = \frac{ \orange{48150}}{3852} \\ \\ \to \pink{\boxed{\sf \red{x = 12.5}\%}}$

Hence gain is 12.5 % .

Answer 2

Answer:

$\boxed{\boxed{\sf\pink{Gain \: percent = 12.5\%}}}$

Step-by-step explanation:

Given:-

• 1st SP = Rs.3852
• 1st gain% = 7%
• 2nd SP = Rs.4050

To find:-

• 2nd gain% = ?

We know that,in gain,

$\star\boxed{\boxed{\sf\green{\dfrac{Gain(SP - CP)}{CP}\times 100 = Gain\%}}}$

$\hookrightarrow\sf \dfrac{SP - CP}{CP} \times 100 = 7 \\\\\hookrightarrow\sf \dfrac{3852 - CP}{CP }\times 100 = 7 \\\\\hookrightarrow\sf 100(3852 - CP) = 7CP \\\\\hookrightarrow\sf 385200 - 100CP = 7CP \\\\\hookrightarrow\sf 100CP + 7CP = 385200 \\\\\hookrightarrow\sf 107CP = 385200 \\\\\hookrightarrow\sf CP =\cancel{\dfrac{385200}{107}} \\\\\hookrightarrow\large{\boxed{\sf\red{CP = Rs.3600 }}}$

$\rule{200}{1}$

Secondly,

• SP = Rs.4050
• CP = Rs.3600

• Gain percent = ?

Now using same formula we get,

$\hookrightarrow\sf Gain\% =\dfrac{4050 - 3600}{3600}\times 100 \\\\\hookrightarrow\sf Gain\% =\dfrac{450}{3600}\times 100 \\\\\hookrightarrow\sf Gain\% =\dfrac{450 \times 100}{3600} \\\\\hookrightarrow\sf Gain\% = \dfrac{45,000}{3600} \\\\\hookrightarrow\large{\boxed{\sf\pink{Gain\% = 12.5 \%}}}$

${\underline{\boxed{\therefore{\sf\blue{Gain\: percent = 12.5\%}}}}}$