Question

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hellooooooooo

the selling price of a toy is rs.1540 if the profit made by the shopkeeper is 40% find the cost price

explain step by step

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

$\text{The cost Price of the toy is Rs.1100}$

$\textbf{\underline{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given :}}}$

Selling Price of the toy = Rs.1540

Profit made by the shopkeeper = 40%

$\textsf{\underline{\underline{To find :}}}$

The cost Price of the toy

$\textsf{\underline{\underline{Solution :}}}$

$\textbf{\large{\underline{Method I =}}}$

Let the C.P of the toy be x

Profit =

$\tt{\implies \: profit\% \: of \: CP}$

$\tt{\implies40\% \: of \: x }$

$\tt{\implies \dfrac{40}{100} \times x }$

$\tt{\implies \dfrac{2}{5}x }$

${\boxed{\bigstar{\sf \:{Profit = \frac{2}{5}x }}}}$

SP = CP + Profit

$\tt{\implies \: SP = x + \dfrac{2}{5}x}$

Convert them into like fraction to add them.

$\tt{\implies SP = \dfrac{5x + 2x}{5} }$

$\tt{\implies \: SP =\dfrac{7x}{5} }$

${\boxed{\bigstar{\sf \: {\tt{\: SP =\dfrac{7x}{5}}}}}}$

According to the question – SP = Rs.1540

$\therefore$ $\tt{1540 = \dfrac{7x}{5}}$

$\tt{\implies1540 = \dfrac{7x}{5} }$

$\tt{\implies1540 \times 5 = 7x}$

$\tt{\implies7700 = 7x}$

$\tt{\implies \: x = \dfrac{7700}{7} }$

$\tt{\implies \: x = 1100}$

${\boxed{\bigstar{\sf \: {CP = Rs.1100}}}}$

$\therefore$$\text{The cost Price of the toy is Rs.1100}$

$\textbf{\large{\underline{METHOD II =}}}$

$\tt{\implies \: CP = \dfrac{100}{(100 + Gain\%)}\times SP }$

$\tt{\implies \: CP = \dfrac{100}{(100 + 40)} \times 1540 }$

$\tt{\implies \: CP = \dfrac{100}{140} \times 1540}$

Cancel the Zero's

$\tt{\implies \: CP = \dfrac{100}{14{\cancel{0}}}\times 154{\cancel{0}}}$

$\tt{\implies \: CP = \dfrac{100}{14} \times 154}$

$\tt{\implies \: CP = \dfrac{15400}{14}}$

$\tt{\implies \: CP = 1100}$

${\boxed{\bigstar{\sf \:{\:CP = Rs.1100}}}}$

$\therefore$$\text{The cost Price of the toy is Rs.1100}$

Answer 2

this is correct and easy approach to understand the concept