Answer
Verified
91.5k+ views
Hint – We are unaware of the cost of a single chair and a single table, so considering the price of a single item as a variable can help . Form two different linear equations by the conditions given in the question.
Let the price of a single chair $ = {\text{ Rs x}}$
Let the price of a single table $ = {\text{ Rs y}}$
Now it’s given that cost of 9 chairs and 3 tables is Rs306, thus the mathematical equation that is formed using this information is
$9x + 3y = 306$………………….. (1)
Now it is also given that cost of 6 chairs and 3 tables is Rs246, thus the mathematical equation that is formed using this information is
$6x + 3y = 246$……………….. (2)
Now subtracting equation (2) and equation (1)
$6x + 3y - 9x - 3y = 246 - 306$
On solving we get
$
- 3x = - 60 \\
\Rightarrow x = 20 \\
$
Now putting x in equation (1)
$
9 \times 20 + 3y = 306 \\
\Rightarrow 3y = 306 - 180 \\
\Rightarrow 3y = 126 \\
\Rightarrow y = 42 \\
$
Now we have the cost of one chair, x=20 and one table, y=40.
Thus now we need to find cost of 6 chairs and 1 table that is the mathematical equation that we need to evaluate is $6x + y$……………………….. (3)
Putting the values of x and y in equation (3)
$6 \times 20 + 42 = 162$
Thus the cost of 6 chairs and 1 table is Rs162
Hence option (b) is correct.
Note – Whenever we face such types of problems the key concept that we need to keep in mind is that we always try and find out the cost of a single item, by forming different linear equations by the information provided in the question. Then apply any of methods of elimination or substitution to solve the equations.
Let the price of a single chair $ = {\text{ Rs x}}$
Let the price of a single table $ = {\text{ Rs y}}$
Now it’s given that cost of 9 chairs and 3 tables is Rs306, thus the mathematical equation that is formed using this information is
$9x + 3y = 306$………………….. (1)
Now it is also given that cost of 6 chairs and 3 tables is Rs246, thus the mathematical equation that is formed using this information is
$6x + 3y = 246$……………….. (2)
Now subtracting equation (2) and equation (1)
$6x + 3y - 9x - 3y = 246 - 306$
On solving we get
$
- 3x = - 60 \\
\Rightarrow x = 20 \\
$
Now putting x in equation (1)
$
9 \times 20 + 3y = 306 \\
\Rightarrow 3y = 306 - 180 \\
\Rightarrow 3y = 126 \\
\Rightarrow y = 42 \\
$
Now we have the cost of one chair, x=20 and one table, y=40.
Thus now we need to find cost of 6 chairs and 1 table that is the mathematical equation that we need to evaluate is $6x + y$……………………….. (3)
Putting the values of x and y in equation (3)
$6 \times 20 + 42 = 162$
Thus the cost of 6 chairs and 1 table is Rs162
Hence option (b) is correct.
Note – Whenever we face such types of problems the key concept that we need to keep in mind is that we always try and find out the cost of a single item, by forming different linear equations by the information provided in the question. Then apply any of methods of elimination or substitution to solve the equations.
Recently Updated Pages
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main
What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main
A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main
Other Pages
Electric field due to uniformly charged sphere class 12 physics JEE_Main
If the distance between 1st crest and the third crest class 11 physics JEE_Main
Derive an expression for maximum speed of a car on class 11 physics JEE_Main
3 mole of gas X and 2 moles of gas Y enters from the class 11 physics JEE_Main
The vapour pressure of pure A is 10 torr and at the class 12 chemistry JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main