✓ Board-verified
Mathematics · 2025 · 4 marks
CBSE 2025 · Region 2 · Set 1 · Q36
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…
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)
(a)
Find the number of chairs and number of tables rented by the school.
OR
(b)
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.
(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.
All Pair of Linear Equations in Two Variables questions2025 question paperNCERT solutions: Pair of Linear Equations in Two VariablesPractice Pair of Linear Equations in Two Variables →
More from Pair of Linear Equations in Two Variables
- In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total score would have…2026
- Equation of a line coincident with 2 · 5 x-2 y=3 is:2026
- Draw the graph of the pair of linear equations x-y+2=0 and 4 x-y-4=0. Calculate the area of the triangle formed by the lines so drawn and the x -axis.2026
- If the system of linear equations 2 x+3 y=7 and 2 a x+(a+b) y=28 have infinite number of solutions, then find the values of ' a ' and ' b '. OR If…2023
- The sum of the areas of two squares is 52 cm^2 and difference of their perimeters is 8 cm. Find the lengths of the sides of the two squares. OR The…2025
- Solve the following pair of equations algebraically: 101 x+102 y=304; 102 x+101 y=305 OR In a pair of supplementary angles, the greater angle exceeds…2025
- Check whether the given system of equations is consistent or not. If consistent, solve graphically. x-2 y=0; 2 x+y=02025
- The value of k for which the system of linear equations x/2+y/3=5 and 2 x+ky=7 is inconsistent, is2026
CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.