CBSE 2025 · Region 2 · Set 1 · Q36 · 4 marks
A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to rent chairs and tables from a local supplier. It finds that rent for each chair is ₹ $\displaystyle 50$ and for each table is ₹ 200. The school spends ₹ $\displaystyle 30,000$ for renting the chairs and tables. Also, the total number of items (chairs and tables) rented are 300.
If the school rents 'x' chairs and 'y' tables, answer the following questions :(i)Write down the pair of linear equations representing the given information.(ii)Find the number of chairs and number of tables rented by the school.If the school wants to spend a maximum of ₹ $\displaystyle 27,000$ on $\displaystyle 300$ items (tables and chairs), then find the number of chairs and tables it can rent.(iii)What is maximum number of tables that can be rented in ₹ $\displaystyle 30,000$ if no chairs are rented?
A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to rent chairs and tables from a local supplier. It finds that rent for each chair is ₹ $\displaystyle 50$ and for each table is ₹ 200. The school spends ₹ $\displaystyle 30,000$ for renting the chairs and tables. Also, the total number of items (chairs and tables) rented are 300.
If the school rents 'x' chairs and 'y' tables, answer the following questions :
(i)
Write down the pair of linear equations representing the given information.
(ii)
Find the number of chairs and number of tables rented by the school.
If the school wants to spend a maximum of ₹ $\displaystyle 27,000$ on $\displaystyle 300$ items (tables and chairs), then find the number of chairs and tables it can rent.
(iii)
What is maximum number of tables that can be rented in ₹ $\displaystyle 30,000$ if no chairs are rented?
Marking-scheme solution
(i) \(\displaystyle \mathrm{x}+\mathrm{y}=300\)
and \(\displaystyle 50 \mathrm{x}+200 \mathrm{y}=30000\) or \(\displaystyle \mathrm{x}+4 \mathrm{y}=600\)
(ii) (a) \(\displaystyle \mathrm{x}+\mathrm{y}=300\) and \(\displaystyle \mathrm{x}+4 \mathrm{y}=600\)
Solving the equations, we get
\[x=200 \text { and } y=100
\]
∴ Number of chairs and tables rented by the school are $\displaystyle 200$ and $\displaystyle 100$ respectively.
OR
(b) \(\displaystyle \mathrm{x}+\mathrm{y}=300\) and \(\displaystyle 50 \mathrm{x}+200 \mathrm{y}=27000\) or \(\displaystyle \mathrm{x}+4 \mathrm{y}=540\)
Solving the equations, we get
\[x=220 \text { and } y=80
\]
∴ Number of chairs and tables rented by the school are $\displaystyle 220$ and $\displaystyle 80$ respectively.
(iii) Number of tables \(\displaystyle =\frac{30000}{200}=150\)
∴ Maximum number of tables that can be rented is $\displaystyle 150$ if no chairs are rented.
Pair of Linear Equations in Two VariablesWord Problems on Linear EquationsApplycase_studymedium
Practice Pair of Linear Equations in Two Variables →All Pair of Linear Equations in Two Variables questions
More from Pair of Linear Equations in Two Variables
- Solve the following pair of equations algebraically: OR In a pair of supplementary angles, the greater angle…2025 · asked 3×
- Assertion: The pair of linear equations px + 3y + 59=0 and 2 x+6 y+118=0 will have infinitely many solutions…2025 · asked 3×
- The line represented by the equation x-y=0 is:2025 · asked 3×
- If x=1 and y=2 is a solution of the pair of linear equations 2 x-3 y+a=0 and 2 x+3 y-b=0, then:2025 · asked 3×
- The value of ' p ' for which the equations p x+3 y=p-3,12 x+p y=p has infinitely many solutions is:2025 · asked 3×
- The cost of 2 kg apples and 1 kg of grapes on a day was found to be ₹ 320. The cost of 4 kg apples and 2 kg…2025 · asked 3×
- A 2-digit number is seven times the sum of its digits and two (2) more than 5 times the product of its…2025 · asked 3×
- The sum of the areas of two squares is 52 cm^2 and difference of their perimeters is 8 cm. Find the lengths…2025 · asked 2×
CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.