Answer
Verified
413.1k+ views
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.
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.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE