Question

13)
A shopkeeper gains 7% by selling a article for 7 3852. If he sells it for?
4050. find his gain percent​

Answer 1

$Given \: Selling \:price \: of \: an \: article \\(s.p) = Rs \: 3852$

$Gain (g) = 7\%$

$Let \:the \:cost \:price \:of \:the \:article = Rs\:x$

$x = \frac{s.p \times 100}{100+g} \\= \frac{3852 \times 100 }{100+7} \\= \frac{385200}{107} \\= Rs \: 3600$

/* According to the problem given */

$If \: selling \: price = Rs \: 4050 ,\\</p><p>c.p = Rs \:3600$

$Gain = s.p - c.p \\= Rs \: 4050 - Rs \: 3600 \\= Rs \: 450$

$Gain \: percentage = \frac{gain}{c.p} \times 100 \\= \frac{450}{3600} \times 100 \\= 12.5 \%$

Therefore.,

$\red {Gain \: percentage} \green {= 12.5 \% }$

•••♪

Answer 2

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

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

$\large\boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \red{Answer}} \purple{\mid} }} } : - \: \\ \\ \to \green{\boxed{\sf \red{x = 12.5}\%}} \:$

$\boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \pink{To \: Find}} \purple{\mid} }} } : - \:$

$\implies \sf \: Gain \: percentage \:$

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

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

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"

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

• $\dag$Hence gain is 12.5 % .

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$