Question

In selling a book for rs 106,there is a profit of 58%. if it is sold for rs 104, then the profit percent will be what

Answer 1

AnswEr :

$\bold{Condition} \begin{cases} \sf{SP=Rs. \: 106} \\ \sf{Profit=58\%} \\\sf{CP = ?}\end{cases}$

$\longrightarrow\sf{SP = CP \times \dfrac{(100 + Profit\%)}{100}}$

$\longrightarrow\sf{106 = CP \times \dfrac{(100 + 58\%)}{100}}$

$\longrightarrow \sf{ \cancel{106} = CP \times \dfrac{ \cancel{158}}{100}}$

$\longrightarrow \sf{ 53 = CP \times \dfrac{79}{100}}$

$\longrightarrow \sf{ 53\times \dfrac{100}{79} = CP }$

$\longrightarrow \boxed{\sf{ CP = Rs. \: 67 }} \: \: \: \: \: \: \: \: \: \: \underline{\text{Approx}}$

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$\bold{New \: Condition} \begin{cases} \sf{CP =Rs. \: 67} \\ \sf{SP = Rs. \: 104} \\ \sf{Profit =?\%}\end{cases}$

$\longrightarrow \sf{SP = CP \times \dfrac{(100 + Profit\%)}{100}}$

$\longrightarrow \sf{104 = 67 \times (100 + Profit\%)}$

$\longrightarrow \sf{104 = 67 \times \dfrac{(100 + Profit\%)}{100}}$

$\longrightarrow \sf{104 \times \dfrac{100}{67} =(100 +Profit\%)}$

$\longrightarrow \sf{ \dfrac{10400}{67} =100 +Profit\%}$

$\longrightarrow \sf{155=100 +Profit\%} \: \: \: \: \: \: \: \: \underline{\text{Approx}}$

$\longrightarrow \sf{155 - 100 = Profit\%}$

$\longrightarrow \large \boxed{ \sf{ Profit\% = 55\%}}$

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჻ Profit Percentage will change into 55%.

Answer 2

Question :-

In selling a book for rs 106,there is a profit of 58%. if it is sold for rs 104, then the profit percent will be what .

Answer:-

$\star \: \red{\boxed{ \sf{ \green{ profit \: \% = 55.038 \: \%}}}} \:$

To Find :-

→ Find percentage of profit.

Formula used :-

$\star \: \boxed{ \sf{ {SP} = CP \bigg( \frac{100 + profit \: \%}{100} \bigg) }}$

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Step - by - step explanation :-

Step (1) :-

Firstly we have to find Cost price (CP) for second step or get profit percentage.

Given that -

• Selling price (SP) = ₹ 104

• Profit = 58 %

• Cost price ( CP ) = ?

Using the given formula ↓

$\rightarrow \: \sf{106 = CP \bigg( \frac{100 + 58}{100} \bigg)} \\ \\ \rightarrow \: \sf{CP = \frac{106 \times 100}{158} } \\ \\ \rightarrow \: \boxed{ \sf{CP \: = 67.08}}$

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Now ,

Step (2) :-

Now we have,

• Selling price (SP) = ₹106

• Cost price (CP) = ₹ 67.08

• Profit = ?

Now again using the given formula ,

then we get,

$\rightarrow \: \sf{104 = 67.08 \bigg( \frac{100 + profit \: \%}{100} \bigg)} \\ \\ \rightarrow \: \sf{\frac{104 \times 100}{67.08} = 100 + profit \: \%} \\ \\ \rightarrow \: \sf{155.038 \: = 100 + profit \: \%} \\ \\ \rightarrow \: \sf{155.038 - 100 = profit \: \%} \\ \\ \rightarrow \: \red{\boxed{ \sf{ profit \: \% = 55.038 \: \%}}}$

Therefore profit percentage on book is

55.038 % .

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Hope it helps you.