Answer
Verified
37.2k+ 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
A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main
Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main
Let f be a twice differentiable such that fleft x rightfleft class 11 maths JEE_Main
Find the points of intersection of the tangents at class 11 maths JEE_Main
For the two circles x2+y216 and x2+y22y0 there isare class 11 maths JEE_Main
IfFxdfrac1x2intlimits4xleft 4t22Ft rightdt then F4-class-12-maths-JEE_Main
Other Pages
An electric bulb has a power of 500W Express it in class 11 physics JEE_Main
Lowering in vapour pressure is highest for A 02 m urea class 11 chemistry JEE_Main
The nitride ion in lithium nitride is composed of A class 11 chemistry JEE_Main
Which of the following Compounds does not exhibit tautomerism class 11 chemistry JEE_Main
Which of the following is a nonreducing sugar A Glucose class 12 chemistry JEE_Main
The ratio of speed of sound in Hydrogen to that in class 11 physics JEE_MAIN