Question

8. A man sold a book at a loss of 20%. If he had sold the book for Rs.12 more, he would have gained 10 percent.Find the cost price of the book.
​

Answer 1

Answer:

hope the answer will be helpfull for u.

Answer 2

Solution :

Let the cost price of the book be Rs.r

A/q

We know that formula of the loss% :

$\boxed{\bf{Loss\%=\frac{C.P.-S.P.}{100} }}}}}}$

$\longrightarrow\rm{20\%=\dfrac{r-S.P.}{r} }\\\\\\\longrightarrow\rm{\dfrac{20}{100} =\dfrac{r-S.P.}{r}}\\\\\\\longrightarrow\rm{20r=100(r-S.P.)}\\\\\\\longrightarrow\rm{20r=100r-100\:S.P.}\\\\\\\longrightarrow\rm{20r-100r=-100\:S.P.}\\\\\\\longrightarrow\rm{-80r=-100\:S.P.}\\\\\\\longrightarrow\rm{S.P.=\cancel{\dfrac{-80r}{-100} }}\\\\\\\longrightarrow\rm{\pink{S.P.=Rs.0.8r}}$

We know that formula of the profit% :

$\boxed{\bf{Gain\%=\frac{S.P.-C.P.}{100} }}}}}}$

$\longrightarrow\rm{10\%=\dfrac{(0.8r+12)-r}{r} }\\\\\\\longrightarrow\rm{\dfrac{10}{100} =\dfrac{0.8r+12-r}{r}}\\\\\\\longrightarrow\rm{100(0.8r+12-r)=10r}\\\\\\\longrightarrow\rm{100(0.2r+12)=10r}\\\\\\\longrightarrow\rm{-20r+1200=10r}\\\\\\\longrightarrow\rm{-20r-10r=-1200}\\\\\\\longrightarrow\rm{-30r=-1200}\\\\\\\longrightarrow\rm{r=\cancel{\dfrac{-1200}{-30} }}\\\\\\\longrightarrow\rm{\pink{r=Rs.40}}$

Thus;

The cost price of the book will be Rs.40 .