Question

Shreya sold his bicycle at gain of 10%. If he had bought it for 10% less and sold it for ₹45 more, he would have gained 25%.Find the cost price of the bicycle.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that cost price of a bicycle of ₹ x

Gain % = 10 %

Now, we know

$\color{green}\boxed{ \rm{ \:Selling \: Price = \frac{(100 + Gain\%) \times Cost \: Price}{100} \: }}$

So, on substituting the values, we get

$\rm \: Selling \: Price \: = \: \dfrac{(100 + 10) \times x}{100}$

$\rm \: Selling \: Price \: = \: \dfrac{(110) \times x}{100}$

$\rm\implies \:Selling \: Price \: = \: \dfrac{11x}{10}$

Now, According to statement, If he had bought it for 10% less and sold it for ₹45 more, he would have gained 25%.

Now,

$\rm \: Cost \: Price = x - 10\% \: of \: x$

$\rm \: = \: x - \dfrac{10}{100} \times x$

$\rm \: = \: x - \dfrac{x}{10}$

$\rm \: = \: \dfrac{10x - x}{10}$

$\rm \: = \: \dfrac{9x}{10}$

$\rm \: Gain \:\% \: = \: 25 \: \%$

$\rm \: Selling \: Price \: = \: \dfrac{11x}{10} + 45$

Now, we know

$\color{green}\boxed{ \rm{ \:Selling \: Price = \frac{(100 + Gain\%) \times Cost \: Price}{100} \: }}$

So, on substituting the values, we get

$\rm \: \dfrac{11x}{10} + 45 = \dfrac{(100 + 25)}{100} \times \dfrac{9x}{10}$

$\rm \: \dfrac{11x + 450}{10} = \dfrac{(125)}{100} \times \dfrac{9x}{10}$

$\rm \: 11x + 450 = \dfrac{5}{4} \times 9x$

$\rm \: 4(11x + 450) = 45x$

$\rm \: 44x + 1800 = 45x$

$\rm \: 44x - 45x = - 1800$

$\rm \: - x = - 1800$

$\color{green}\rm\implies \:x = 1800$

Hence, the cost price of bicycle = ₹ 1800

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$