Question

A merchant lost 5% by selling an article for 26.65. If he sells it for*31.05. Find his gain percentage .​

Answer 1

Given :-

Loss percentage = 5%

Ist selling price = 26.65

2nd selling price = 31.05

To Find :-

His gain percentage.

Solution :-

Let the cost price be x

$\sf{\huge{\bold{\boxed{\blue{1st\: Case}}}}}$

Cost price = x

Selling price = 26.65

Loss percentage = 5%

We know that,

Total loss = 5% of CP

${\sf{=\: 5\: \%\: of\: x}}$

${\sf{=\: {\dfrac{5\: \times\: x}{100}}}}$

${\sf{=\: {\dfrac{x}{20}}}}$

Selling price = CP - Loss

${\sf{=\: x\: -\: {\dfrac{x}{20}}}}$

${\sf{=\: {\dfrac{20x\: -\: x}{20}}}}$

${\sf{=\: {\dfrac{19x}{20}}}}$

But also given that, SP = 26.65

Therefore,

According to question,

${\sf{26.65\: =\: {\dfrac{19x}{20}}}}$

${\sf{x\: =\: {\dfrac{26.65\: \times\: 20}{19}}}}$

${\sf{x\: =\: {\bold{28.05}}}}$

Therefore, CP = 28.05

$\sf{\huge{\bold{\boxed{\blue{2nd\: Case}}}}}$

CP = 28.05

SP = 31.05

Total profit = SP - CP

= 31.05 - 28.05

= 3

We know that,

${\sf{Profit\: Percentage\: =\: {\dfrac{Profit\: \times\: 100}{CP}}}}$

On inserting the values in the formula

We get ,

${\sf{Profit\: Percentage\: =\: {\dfrac{3\: \times\: 100}{28.05}}}}$

${\sf{Profit\: Percentage\: =\: {\bold{10.69}}}}$

Therefore, profit percentage is 10.69 %

Answer 2

${\bold{\sf{\underline{Understanding \: the \: question}}}}$

⸙ As we already understand that this question is from a very interesting chapter of mathematics - “ Profit and loss ”. This question says that a merchant sold an article for Rupees 26.65 on the loss of 5 % to him. Now the question says that if he sell it for Rupees 31.05 then what is the gain percentage ?

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

⸙ Selling price of an article = Rupees 26.65

⸙ Loss on selling price of article of Rupees 26.65 = 5 %

⸙ New ( assuming atq ) selling price of article = 31.05 Rupees

${\bold{\sf{\underline{To \: find}}}}$

⸙ Gain price on new S.P of article.

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

⸙ Gain price on new S.P of article = 10.69 %

${\bold{\sf{\underline{Using \: concepts \: (atq)}}}}$

➨ Formula to find Selling price

➨ Formula to find Total loss

➨ Total profit

➨ Gain percentage

${\bold{\sf{\underline{Using \: formulas \: (atq)}}}}$

➨ Selling price = CP - loss

➨ Total loss = Loss % of CP

➨ Total profit = SP - CP

➨ Gain percentage = Gain × 100 / CP

${\bold{\sf{\underline{Full \: solution}}}}$

~ Viewing total loss

➥ Total loss = Loss % of CP

➥ Total loss = 5 % of CP

➥ Total loss = 5 % × CP

➥ Total loss = 5 × CP / 100

➥ Total loss = CP / 20

~ Finding cost price

➥ Selling price = CP - loss

➥ Selling price = CP - CP/20

• Taking LCM

➥ Selling price = 20 CP - CP / 20

➥ Selling price = 20 CP - 1 CP / 20

➥ Selling price = 19 CP / 20

Now atq

➥ Given SP = Finded SP

➥ 26.65 = 19 CP / 20

• Cross multiplying the digits

➥ CP = 26.65 × 20 / 19

➥ CP = 533 / 19

➥ CP = 28.05 Rupees

~ Viewing total profit

➥ Total profit = SP - CP

➥ Total profit = 31.05 - 28.05

➥ Total profit = 3 Rupees

~ Seeming gain %

➥ Gain percentage = Gain × 100 / CP

➥ Gain percentage = 3 × 100 / 28.05

➥ Gain percentage = 300 / 28.05

➥ Gain percentage = 10.69 %

• Henceforth, the gain percentage is 10.69 %

${\bold{\sf{\underline{Knowledge \: booster}}}}$

Some formulas related to Profit and Loss -

$\boxed{\begin{minipage}{7cm}\bigstar \:\underline{\textbf{Profit and Loss Formulas :}}\\\\ \\ \sf {\textcircled{\footnotesize\textsf{1}}} \:S.P. = \sf \bigg\lgroup\dfrac{100 + Profit \%}{100}\bigg\rgroup \times 100 \\\\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:C.P. = \sf \dfrac{S.P. \times 100}{100 + Profit \%} \\\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Profit = \sf \dfrac{Profit \% \times C.P.}{100} \\\\\\ \sf{\textcircled{\footnotesize\textsf{4}}} \: \:Profit (gain) = S.P. - C.P. \\\\\\\sf{\textcircled{\footnotesize\textsf{5}}} \: \: \sf Profit \% = \dfrac{Profit}{C.P.} \times 100 \end{minipage}}$

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