A cycle is sold for Rs. 880 at a loss of 20%. For how much it should be sold to gain 10%?

 Hint: In this problem we are given the selling price not the cost price. So, formula for loss is expressed in terms of cost and selling price and then we obtain the actual cost price of the cycle. Once the cycle’s cost price is obtained then we can calculate the price for selling it for the profit of 10%. This will be our final answer.

Complete step by step answer:
As per the problem, the cycle is sold at Rs. 880. Hence, the selling price of the cycle would be Rs. 880.
The formula for evaluation of loss is stated as:
$%loss=\dfrac{C.P.-S.P.}{C.P.}\times 100$
The cycle is sold at a loss of 20%. Now, the cost price is evaluated using the above stated formula.
$\begin{align}
  & 20=\dfrac{C.P.-880}{C.P.}\times 100 \\
 & \dfrac{C.P.-880}{C.P.}=\dfrac{1}{5} \\
\end{align}$
On solving further, we get cost price as,
$\begin{align}
  & 5C.P.-4400=C.P. \\
 & C.P.=\dfrac{4400}{4}=1100 \\
\end{align}$
Hence, the cycle was bought at a price of Rs. 1100.
Now, we want to gain a profit of 10% on selling the bicycle. To do so, we evaluate the selling price using the profit formula.
The formula for evaluation of profit is stated as:
$%gain=\dfrac{S.P.-C.P.}{C.P.}\times 100$
The cycle is sold for a gain of 10%. Now, the selling price is evaluated using the above stated formula.
$\begin{align}
  & 10=\dfrac{S.P.-C.P.}{C.P.}\times 100 \\
 & \dfrac{S.P.-1100}{1100}=\dfrac{1}{10} \\
 & S.P=1100+110 \\
 & S.P=1210 \\
\end{align}$
So, to gain a profit of 10% cycle must be sold at a price of Rs. 1210.

Note: The key step for solving such a question is to express the cost price and selling price in terms of loss or profit percent. This problem is related to statement based solving procedure. This knowledge is important for traders to calculate profit or loss related to items.