Class 10
[CBSE 2025] The students of a class are made to stand equally in rows. If 3 students are extra in . . .
CBSE 2025
Solution :
Let the number of students in each row = x
and the number of rows = y
Total number of students = xy
ATQ
(x+3)(y-1)=xy
x(y-1)+3(y-1)=xy
xy-x+3y-3=xy
-x+3y-3=0
-x+3y=3 — (1)
Also
(x-3)(y+2)=xy
x(y+2)-3(y+2)=xy
xy+2x-3y-6=xy
2x-3y-6=0
2x-3y=6 — (2)
Solving equation (1) and (2)
-x+3y=3
2x-3y=6
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x+0y=9
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x=9
putting in equation (1)
-9+3y=3
3y=3+9
3y=12
y=12/3
y=4
Number of students in each row = 9
and the number of rows = 4
Total number of students
=xy
=9×4
=36
Hence, the total number of students in the class is 36.
[CBSE 2025] The perimeter of a rectangle is 70 cm. The length of the rectangle is 5 cm . . .
Solution :
ATQ
Perimeter of rectangle = 2(l+b)
70 = 2(x+y)
70/2=x+y
35=x+y
x+y=35 — (1)
Also,
x=5+2y
x-2y=5 — (2)
Solving equation (1) and (2)
- + -
---------------
0 +3y=30
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3y=30
y=10
x=35-10
x=25
The two angles of a right angled triangle other than . . .
ATQ
x+y+90°=180° (ASP)
x+y=180°-90°
x+y=90° — (1)
Also
x:y=2:3
x/y=2/3
3x=2y
3x-2y=0 — (2)
Solving equation (1) and (2)
2x+2y=180°
3x-2y=0
----------------
5x+0y=180
----------------
5x=180
x=180/5
x=36°
putting in equation (1)
36°+y=90°
y=90°-36°
y=54°
Hence, the required values of two angles is 36° and 54°.
The area of a rectangle gets reduced by 9 square units . . .
= xy square units.
x(y+3)-5(y+3)=xy-9
xy+3x-5y-15=xy-9
3x-5y=6 — (1)
x(y+2)+3(y+2)=xy+67
xy+2x+3y+6=xy+67
2x+3y+6=67
2x+3y=67-6
2x+3y=61 — (2)
- - -
-----------------
0x-19y=-171
-----------------
-19y=-128
19y=128
y=128/19
y=9
3x-5(9)=6
3x-45=6
3x=6+45
3x=51
x=51/3
x=17
Hence, length of rectangle is 17 units and breadth of rectangle is 9 units.
[CBSE 2025] √2x+√3y = 5, √3x-√8y =-√6 Solve for x and y . . .
√6x+3y=5√3
- + +
---------------------------
0x + 7y =5√3+√12
---------------------------
7y=5√3+2√3
7y=7√3
y=7√3/7
y=√3
√2x+3=5
√2x=5-3
√2x=2
x=2/√2
x=√2
[CBSE 2025] 30x+44y=10, 40x+55y=13 Solve the following system of equations algebraically . . .
120x+176y=40
120x+165y=39
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0x + 11y = 1
----------------------
11y=1
y=1/11
30x+44y=10
30x+44(1/11)=10
30x=10-4
30x=6
x=6/30
Hence, x=1/5 and y=1/11.
[CBSE 2025] Solve the following system of equations algebraically . . .
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100x+100y=300
x+y=300/100
- - -
-----------------------
-26x+26y=-26
-x+y=-26/26
-x+y=-1 — (4)
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0 +2y=2
x+1=3
x=3-1
x=2
Click Here for Answer
x=2, y=1
Click Here for Answer
x=2, y=1
[CBSE 2025] A school is organizing a grand cultural event to show . . .
Case Study Based Question on Chapter - 3
(Pair of Linear Equations in Two Variables)
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 ₹ 50 and for each table is ₹ 200. The school spends ₹ 30,000 for renting the chairs and tables. Also, the total number of items (chairs and tables) rented are 300.

OR
Let number of chairs = x
Also
Solving equation (1) and (2)
- - -
----------------
0+3y=300
----------------
x+100=300
- - -
---------------
0+3y=240
---------------
y=?
y=150
[CBSE 2025] A bag contains some red and blue balls . . .
(10/100)x + (20/100)y = 24
x/10 + 2y/10 = 24
(x+2y)/10 = 24
x+2y = 240 — (1)
3x-y = 20 — (2)
Solving equation (1) and (2)
7x + 0 = 280
---------------------
7x=280
x=280/7
x=40
120-y=20
120-20 = y
100 = y
y = 100
Hence, number of red balls = 40 and number of blue balls = 100.
[CBSE 2025] Vijay invested certain amounts of money in two schemes A and . . .
Question : Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. He received 1,860 as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received 20 more as annual interest. How much money did he invest in each scheme ?
CBSE 2025
Solution :
Let amount invested by Vijay at 8% interest rate be ₹ x
and the amount invested by Vijay at 9% interest rate be ₹ y
We know,
Simple Interest (SI) = [Principle×Rate×Time]/100
Here Time is 1 Year in both the case.
SI on Amount of ₹ x which is invested at 8% interest rate
= [Principle×Rate×Time]/100
= [x×8×1]/100
= 8x/100
SI on Amount of ₹ y which is invested at 9% interest rate
= [Principle×Rate×Time]/100
= [y×9×1]/100
= 9y/100
ATQ
8x/100 + 9y/100 = 1860
(8x+9y)/100 = 1860
8x+9y=186000 — (1)
Similarly
9x+8y= (1860+20)×100
9x+8y=188000 — (2)
Solving equation (1) and (2)
[8x+9y=186000] ×9
[9x+8y=188000] ×8
72x+81y=1674000
72x+64y=1504000
- - -
----------------------------
0 + 17y = 170000
----------------------------
17y=170000
y=170000/17
y=10000
putting in equation (1)
8x+9[10000]=186000
8x+90000=186000
8x=186000-90000
8x=96000
x=96000/8
x=12000
Hence, money invested in scheme A is ₹12000 and scheme B is ₹10000.