Question

A bicycle was sold at a profit of12%. Had it been sold for 16 rs. More the profit would have been 20%. Find the sellung price of the bicycle. ​

Answer 1

AnswEr :

Let the CP of Bicycle be Rs. x and gained Profit Percent of 12%.

$\longrightarrow\tt SP = CP \times (100 + Profit)\%\\\\\\\longrightarrow\tt SP = x \times (100 + 12)\%\\\\\\\longrightarrow\tt SP = x \times 112\%\\\\\\\longrightarrow\tt SP = x \times \dfrac{112}{100}\\\\\\\longrightarrow\tt SP = \dfrac{112x}{100}$

$\rule{200}{1}$

If it had been sold for Rs. 16 more, then Profit Percent would have been 20%.

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\tt SP + 16 = CP \times (100 + Profit)\%\\\\\\:\implies\tt \dfrac{112x}{100} + 16= x \times (100 + 20)\%\\\\\\:\implies\tt \dfrac{112x}{100} + 16 =x \times 120\%\\\\\\:\implies\tt \dfrac{112x}{100} + 16= \dfrac{120x}{100}\\\\\\:\implies\tt 16= \dfrac{120x}{100} - \dfrac{112x}{100}\\\\\\:\implies\tt 16 =\dfrac{8x}{100}\\\\\\:\implies\tt \dfrac{16 \times 100}{8} = x\\\\\\:\implies\tt 2 \times 100 = x\\\\\\:\implies\tt x = Rs. \:200$

$\rule{150}{2}$

$\underline{\bigstar\:\textsf{Selling Price :}}$

$\dashrightarrow\:\:\tt Selling\:Price = \dfrac{112x}{100}\\\\\\\dashrightarrow\:\:\tt Selling\:Price = \dfrac{112 \times 200}{100}\\\\\\\dashrightarrow\:\:\tt Selling\:Price = 112 \times 2\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt Selling\:Price = Rs.\:224}}$

⠀

$\therefore\:\underline{\textsf{Selling Price of Bicycle is \textbf{Rs. 224}}}.$

$\rule{200}{2}$

$\boxed{\begin{minipage}{6.5 cm}\underline{\text{Some Important Formulae Related to it :}}\\ \\ SP=CP\times(100+\sf Profit)\%\\ \\SP=CP\times(100-Loss)\%\\ \\Profit\%=\dfrac{Profit}{CP}\times100 \\ \\Loss\%=\dfrac{Loss}{CP}\times100\end{minipage}}$

Answer 2

$\huge\star{\purple{\underline{\mathfrak{Answer :-}}}}$

${\huge\tt\bf{Given}}\begin{cases}\textsf{Profit by selling bicycle= 12\%}\\\textsf{If it have been sold for Rs.16 more, profit= 20\%}\end{cases}$

${\huge\tt\bf{To\: Find :-}}$

• The selling price of the bicycle

${\huge\tt\bf{Solution :-}}$

Let the cost price be x.

We know that,

$\huge{\boxed{\red{\tt{SP=CP\times(100+Profit)\%}}}}$

So,

$\longrightarrow\tt{SP=x\times(100+12)\%}$

$\longrightarrow\tt{SP=x\times(112)\%}$

$\longrightarrow\tt{SP=\dfrac{112x}{100}}$......(1)

$\rule{200}2$

Now, it is given that if the bicycle would have been sold for Rs. 16 more, the profit percent would have been 20 %.

So,

$\longrightarrow\tt{SP+ Rs.16=x\times(100+20)\%}$

$\longrightarrow\tt{SP+ Rs.16=x\times(120)\%}$

$\longrightarrow\tt{SP+ Rs.16=\dfrac{120x}{100}}$

Now, by using equation 1,

$\longrightarrow\tt{\dfrac{112x}{100}+ Rs.16=\dfrac{120x}{100}}$

Now, solving further to find the value of x,

$\longrightarrow\tt{Rs.16=\dfrac{120x}{100}-\dfrac{112x}{100}}$

$\longrightarrow\tt{Rs.16=\dfrac{120x-112x}{100}}$

$\longrightarrow\tt{Rs.16=\dfrac{8x}{100}}$

$\longrightarrow\tt{x=\dfrac{16\times 100}{8}}$

$\longrightarrow\tt{\pink{x=Rs.200}}$....(2)

$\rule{200}2$

Now, finding the selling price of the bicycle with the help of equation 1 and 2,

$\mapsto\tt{SP=\dfrac{112\times \cancel{200}\:\:2}{\cancel{100}}}$

$\huge\mapsto{\boxed{\tt{\orange{SP=Rs.224}}}}$

Hence, the selling price of the bicycle is Rs. 224.

$\rule{200}2$

Some important Formulae:-

$\leadsto\tt{Cost\:Price\:(CP)=Buying\:Price+Overhead\:expenses}$

$\leadsto\tt{SP=CP+(100+Profit)\%}$

$\leadsto\tt{SP=CP+(100-Loss)\%}$

$\leadsto\tt{Profit\:\%=\dfrac{Profit}{CP}\times 100}$

$\leadsto\tt{Loss\:\%=\dfrac{Loss}{CP}\times 100}$

$\leadsto\tt{Discount=Marked\:Price-Sales\:Price}$

$\rule{200}4$