Question

An object is sold at a profit of 10%<. what is the ratio of it's cost price to sale price​

Answer 1

$\bf \: \underline{Given} :$ ↴

$\sf \: An \: object \: is \: sold \: at \: a \: gain \: of \: 10 \: \%$

$\bf \: \underline{To \: find }:$ ↴

$\sf \: We \: have \: to \: find \: the \: ratio \: of \: it's \: C.P\: to \: S.P$

$\sf \: \underline{ \underline{Solution}}$

$\sf \: Let \: the \: cost \: price \: be \: z.$

$\: \boxed{ \red{ \sf \: Profit = 10 \: \% \: of \: CP}}$

$\implies \: \sf \: Profit = 10 \: \% \: of \: z$

$\implies \: \sf \: Profit = z \times \dfrac{10}{100}$

$\implies \: \sf \: Profit = z \times \dfrac{1\!\!\!\not0}{10\!\!\!\not0}$

$\implies \: \sf \: Profit = Rs. \: \dfrac{z}{10}$

$\: \boxed{ \red{ \sf S.P = Cost \: price + Profit} }$

$\implies \: \sf \: S.P = z \: + \: \dfrac{z}{10}$

$\implies \:\sf \: S.P = \dfrac{10z + z}{10}$

$\implies \: \sf \: S.P = Rs. \: \dfrac{11z }{10}$

$\sf \: \underline{Now, \: Ratio \: of \: C.P \: to \: S.P \: is} :$

$\sf \: \longmapsto \: \boxed{ \red{ \sf \dfrac{Cost \: price }{ Selling \: price}} }$

$\sf \: Putting \: the \: values,$

$\sf \: \implies \: \dfrac{z}{ \dfrac{11z }{10}}$

$\sf \: \implies \: z \: \div \: \dfrac{11z }{10}$

$\sf \: \implies \: z \: \div \: \dfrac{10 }{11z}$

$\sf \: \implies \: \!\!\!\not{z } \: \div \: \dfrac{10 }{11\!\!\!\not{z}}$

$\sf \: \implies \dfrac{10}{11}$

$\underline{ \boxed{ \pink{\sf \: Hence, \: the \: ratio \: of\: it's \: C.P \: to \: S.P \: is \: 10 : 11}}}$