Answer
Verified
421.5k+ views
Hint: To solve the question, we have to mathematically represent the given information to get a relation between the length of original cloth and the cost per meter.
Complete step-by-step answer:
Let x, y be the length of the piece of cloth and the cost of the piece per meter respectively.
Given
The cost of a piece of cloth is equal to Rs. 200.
The calculated cost of a piece of cloth = xy.
\[\Rightarrow 200=xy\] …. (1)
The cost remains unchanged when the cloth is 5 meters longer and the cost of each meter of cloth is Rs. 2 less.
\[\Rightarrow 200=(x+5)(y-2)\]
Thus, we get \[xy=(x+5)(y-2)\]
By solving the above equation, we get
\[xy=xy+5y-2x-10\]
\[5y=2x+10\]
By substituting the above equation in equation (1) we get
\[5\left( \dfrac{200}{x} \right)=2x+10\]
\[1000=x(2x+10)\]
\[2{{x}^{2}}+10x-1000=0\]
\[{{x}^{2}}+5x-500=0\]
\[\left( x-20 \right)\left( x+25 \right)=0\]
\[\Rightarrow x=20,-25\]
The measurement of the cloth cannot be negative. Thus, x = 20 meters.
By using equation (1) we get
\[200=20y\]
\[\Rightarrow y=10\] rupees per meter.
Thus, the original piece of cloth is 20 meters long in length and the rate per meter of the cloth is 10 rupees per meter.
Note: The possibility of the mistake can be at forming the right equations based on the given information. The other possibility of mistake can be, using all the calculated value obtained from solving the quadratic expression, cost and the length of cloth can never be negative. The alternative method of solving can be using factorization method for 200, where cost per metre and length of cloth can be guessed as 20, 10. By substituting values in the second equation derived from the given information and using a hit and trial method we can arrive at an answer.
Complete step-by-step answer:
Let x, y be the length of the piece of cloth and the cost of the piece per meter respectively.
Given
The cost of a piece of cloth is equal to Rs. 200.
The calculated cost of a piece of cloth = xy.
\[\Rightarrow 200=xy\] …. (1)
The cost remains unchanged when the cloth is 5 meters longer and the cost of each meter of cloth is Rs. 2 less.
\[\Rightarrow 200=(x+5)(y-2)\]
Thus, we get \[xy=(x+5)(y-2)\]
By solving the above equation, we get
\[xy=xy+5y-2x-10\]
\[5y=2x+10\]
By substituting the above equation in equation (1) we get
\[5\left( \dfrac{200}{x} \right)=2x+10\]
\[1000=x(2x+10)\]
\[2{{x}^{2}}+10x-1000=0\]
\[{{x}^{2}}+5x-500=0\]
\[\left( x-20 \right)\left( x+25 \right)=0\]
\[\Rightarrow x=20,-25\]
The measurement of the cloth cannot be negative. Thus, x = 20 meters.
By using equation (1) we get
\[200=20y\]
\[\Rightarrow y=10\] rupees per meter.
Thus, the original piece of cloth is 20 meters long in length and the rate per meter of the cloth is 10 rupees per meter.
Note: The possibility of the mistake can be at forming the right equations based on the given information. The other possibility of mistake can be, using all the calculated value obtained from solving the quadratic expression, cost and the length of cloth can never be negative. The alternative method of solving can be using factorization method for 200, where cost per metre and length of cloth can be guessed as 20, 10. By substituting values in the second equation derived from the given information and using a hit and trial method we can arrive at an answer.
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
Select the word that is correctly spelled a Twelveth class 10 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE