Question

(8) By selling an article for Rs. 384, a
shopkeeper incurs a loss of 4%. At what
price should he sell the article to gain 10%
?​

Answer 1

Answer :

The article should be sold at ₹440 to gain 10%

Explanation :

S. P. (selling price) of the article : ₹384

Loss incurs = 4%

For selling it in 10% profit we need to calculate the C. P. (Cost price)

Using the formula :

${\underline { \boxed{ {\sf C. P. = \dfrac{100}{100 - loss\%} \times S. P. }}}}$

Substitute the given values :

$\sf \dashrightarrow \dfrac{100}{100 - 4} \times 384$

$\sf \dashrightarrow \frac{100}{ \cancel{96}} \times \cancel{384}$

$\sf \dashrightarrow 100 \times 4$

$\sf \dashrightarrow 400$

$\sf \therefore\underline{The \: CP \: is \: ₹400}$

Now, calculate 10% profit in S. P.

Using the formula :

$\sf \dashrightarrow S P = \dfrac{100 + profit\%}{100} \times CP$

Where,

• C. P. is ₹400
• profit is 10%

On substituting the suitable values :

$\sf \dashrightarrow \dfrac{100 + 10}{100} \times 400$

$\sf \dashrightarrow \frac{110}{100} \times 400$

$\sf \dashrightarrow 110 \times 4$

$\sf \dashrightarrow 440$

$\sf \therefore \underline{Required \: anwer : 440}$

Answer 2

Answer:

${\Large{\underline{\frak{\pmb{Given}}}}}$

• ➥ By selling an article for Rs. 384, a shopkeeper incurs a loss of 4%

⠀⠀⠀⠀⠀⠀⠀⠀⠀

${\Large{\underline{\frak{\pmb{To \: Find}}}}}$

• ➥ What price should he sell the article to gain 10% ?

⠀⠀⠀⠀⠀⠀⠀⠀⠀

${\Large{\underline{\frak{\pmb{Using \: Formula }}}}}$

$\bigstar\: \sf \purple{ C.P} = \pink{\dfrac{100}{100-loss\%} \times S.P}$

$\bigstar \: \sf \purple{ S.P} = \pink{\dfrac{100 + Profit\%}{100} \times C.P}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀

${\Large{\underline{\frak{\pmb{Solution }}}}}$

✒ Finding the Cost Price of Article.

${: \blue\implies\sf \pink{ C.P} = \purple{\dfrac{100}{100-loss\%} \times S.P}}$

♛ Here

• ➥ S.P = ₹384
• ➥ Loss % = 4%

⠀⠀⠀⠀⠀⠀⠀⠀⠀

➠ On Substituting the values

${: \blue\implies\sf \pink{ C.P} = \purple{\dfrac{100}{100-4} \times 384}}$

${: \blue\implies \sf \pink{ C.P} = \purple{\dfrac{100} {\cancel{94}} \times \cancel{384}}}$

${:\blue \implies\sf \pink{ C.P} = \purple{100 \times 4}}$

${: \blue\implies\sf \pink{ C.P} = \purple{400}}$

$\: \: \: \: \: \: \: \: \: \large \star \: {\underline{\boxed{\sf{\pmb{ \pink{ C.P} ={ \purple{400 }}}}}}} \: \star$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

✒ Now Finding Selling Price to gain 10%.

${:\blue\implies\sf \pink{ S.P} = \purple{\dfrac{100 + Profit\%}{100} \times C.P}}$

♛ Here

• ➥ C.P = ₹400
• ➥ Profite % = 10%

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➠ On Substituting the values

$:\implies \sf \pink{ S.P} = \purple{\dfrac{100 +10}{100} \times 400}$

$:\implies\sf \pink{ S.P} = \purple{\dfrac{110}{ \cancel{100}} \times \cancel{400}}$

$:\implies\sf \pink{ S.P} = \purple{110 \times 4}$

$:\implies\sf \pink{ S.P} = \purple{440}$

$\: \: \: \: \: \: \: \: \: \star \: {\large {\underline{ \boxed {\sf{\pmb{\pink{ S.P} = \purple{440}}}}}}} \: \star$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

${\large{\underline{\frak{\pmb{Therefore }}}}}$

• ➥ The price should be ₹440 gain 10%.

⠀⠀⠀⠀⠀⠀⠀⠀⠀

${\Large{\underline{\frak{\pmb{Additional \: Information }}}}}$

$\begin{gathered}\small\boxed{\begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P – C.P} \\ \\ \bigstar \:\sf{Loss = C.P – S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100+Gain\%} \times S.P} \\ \\\bigstar \: \sf{ S.P = \dfrac{100-loss\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100-loss\%} \times S.P}\end{array}}\end{gathered}$