Answer
Verified
420.3k+ views
Hint: Assume a variable for the list price of the watch and then calculate the price after 10 % discount. Then using the formula for gain percent, which is \[\dfrac{{Gain}}{{CP}} \times 100\% \], equate the list price and find the value of the list price.
Complete step-by-step answer:
The cost price of the watch is Rs. 450.
The list price of the watch is the selling price of the watch and let it be Rs. X.
After a discount of 10 %, the value of the selling price will be reduced by 10 % of the selling price.
Hence, the reduced selling price is given as:
\[SP = x - 10\% ofx\]
Simplifying, we get:
\[SP = x - \dfrac{{10}}{{100}}x\]
\[SP = x - 0.1x\]
\[SP = 0.9x...........(1)\]
The gain is the difference between the selling price and the cost price. The gain by selling the wrist watch at a discount of 10 % is given as follows:
Gain = SP – CP
Gain = \[0.9x - 450..........(2)\]
The formula for gain percent is given as follows:
\[Gain\% = \dfrac{{Gain}}{{CP}} \times 100\% \]
It is given that the gain percent is 10 %. Hence, using equation (2), we get:
\[10\% = \dfrac{{0.9x - 450}}{{450}} \times 100\% \]
Simplifying, we have:
\[10 = \dfrac{{0.9x - 450}}{9} \times 2\]
Taking 9 in the denominator to the other side, we have:
\[90 = (0.9x - 450) \times 2\]
Simplifying, we have:
\[90 = 1.8x - 900\]
Taking 900 to the other side, we have:
\[90 + 900 = 1.8x\]
\[990 = 1.8x\]
Solving for x, we have:
\[x = \dfrac{{990}}{{1.8}}\]
\[x = Rs.500\]
Hence, the original list price of the wristwatch is Rs. 500.
Hence, the correct answer is option (a).
Note: You can also solve the question backward starting by finding the gain, then the discounted selling price, then the original selling price using the discount percentage.
Complete step-by-step answer:
The cost price of the watch is Rs. 450.
The list price of the watch is the selling price of the watch and let it be Rs. X.
After a discount of 10 %, the value of the selling price will be reduced by 10 % of the selling price.
Hence, the reduced selling price is given as:
\[SP = x - 10\% ofx\]
Simplifying, we get:
\[SP = x - \dfrac{{10}}{{100}}x\]
\[SP = x - 0.1x\]
\[SP = 0.9x...........(1)\]
The gain is the difference between the selling price and the cost price. The gain by selling the wrist watch at a discount of 10 % is given as follows:
Gain = SP – CP
Gain = \[0.9x - 450..........(2)\]
The formula for gain percent is given as follows:
\[Gain\% = \dfrac{{Gain}}{{CP}} \times 100\% \]
It is given that the gain percent is 10 %. Hence, using equation (2), we get:
\[10\% = \dfrac{{0.9x - 450}}{{450}} \times 100\% \]
Simplifying, we have:
\[10 = \dfrac{{0.9x - 450}}{9} \times 2\]
Taking 9 in the denominator to the other side, we have:
\[90 = (0.9x - 450) \times 2\]
Simplifying, we have:
\[90 = 1.8x - 900\]
Taking 900 to the other side, we have:
\[90 + 900 = 1.8x\]
\[990 = 1.8x\]
Solving for x, we have:
\[x = \dfrac{{990}}{{1.8}}\]
\[x = Rs.500\]
Hence, the original list price of the wristwatch is Rs. 500.
Hence, the correct answer is option (a).
Note: You can also solve the question backward starting by finding the gain, then the discounted selling price, then the original selling price using the discount percentage.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
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
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the type of food and mode of feeding of the class 11 biology CBSE
Name 10 Living and Non living things class 9 biology CBSE