# The cost of 9 chairs and 3 tables is Rs306, while the cost of 6 chairs and 3 tables is Rs246.Then the cost of 6 chairs and 1 table is

$

(a){\text{ Rs 161}} \\

(b){\text{ Rs 162}} \\

(c){\text{ Rs 169}} \\

(d){\text{ Rs 175}} \\

$

Last updated date: 17th Mar 2023

•

Total views: 307.2k

•

Views today: 3.86k

Answer

Verified

307.2k+ 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

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Write an application to the principal requesting five class 10 english CBSE

Tropic of Cancer passes through how many states? Name them.

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE

What is per capita income

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India