Question

By selling a book for R.s 22 the shopkeeper gains 10 % find the C. C of the book

Answer 1

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

$\text{The CP of the book is Rs.20}$

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

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

Selling Price of the Book = Rs.22

Gain % = 10%

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

The cost Price of the Book

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

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

$\sf{\implies \: CP = \dfrac{100}{(100 + 10\%) } \times \: 22 }$

$\sf{\implies \: CP = \dfrac{100}{110 } \times \: 22}$

$\sf{\implies \: CP = \dfrac{10{\cancel{0}}}{11{\cancel{0 }}} \times \: 22}$

$\sf{\implies \: CP = \dfrac{10}{11 } \times \: 22}$

$\sf{\implies \: CP = \dfrac{220}{11}}$

$\sf{\implies \: CP = 20}$

$\large{\boxed{\bigstar{\sf \: { CP = 20}}}}$

$\therefore$$\text{The CP of the book is Rs.20}$

$\textbf{\large{\underline{Verification :-}}}$

$\sf{\implies \: 20 = \dfrac{100}{(100 + 10\%) } \times \: 22 }$

$\sf{\implies \: 20 = \dfrac{100}{110 } \times \: 22}$

$\sf{\implies \: 20 = \dfrac{10{\cancel{0}}}{11{\cancel{0 }}} \times \: 22}$

$\sf{\implies \: 20 = \dfrac{10}{11 } \times \: 22}$

$\sf{\implies \: 20 = \dfrac{220}{11}}$

$\sf{\implies \: 20 = 20}$

${\boxed{\bigstar{\sf \: { LHS = RHS}}}}$

$\therefore$$\text{The CP of the book is Rs.20}$