Question

# A tricycle is sold at a gain of 16%. Had it been sold for Rs 100 more, the gain would have been 20 %. Find the C.P. of the tricycle.

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Hint: We will assume the cost price of the tricycle as Rs.x. Then, we will use the formula, $gain\%=\dfrac{gain}{C.P}\times 100$ to get the value of gain from it and then we will use the formula, gain = SP - CP and get CP from there and then again on substituting the value of gain and CP in the formula of gain% and we will get the value of x from there.

\begin{align} & \Rightarrow gain\%=\dfrac{gain}{C.P}\times 100 \\ & \Rightarrow 16=\dfrac{gain}{x}\times 100 \\ & \Rightarrow gain=\dfrac{16x}{100}=\dfrac{4x}{25} \\ \end{align}
\begin{align} & \Rightarrow gain=\text{ S}.P\text{ }-C.P. \\ & \Rightarrow \dfrac{4x}{25}=S.P.-x \\ & \Rightarrow S.P.=\dfrac{29x}{25} \\ \end{align}
\begin{align} & \Rightarrow gain\%=\dfrac{gain}{C.P}\times 100 \\ & \Rightarrow 20=\dfrac{S.P.-C.P.}{x}\times 100 \\ & \Rightarrow 20=\dfrac{\dfrac{29x}{25}+100-x}{x}\times 100 \\ & \Rightarrow 1=\dfrac{\dfrac{4x}{25}+100}{x}\times 5 \\ & \Rightarrow x=\dfrac{4x}{5}+500 \\ & \Rightarrow \dfrac{x}{5}=500 \\ & \Rightarrow x=Rs.2500 \\ \end{align}