✓ Board-verified
Mathematics · 2025 · 5 marks
CBSE 2025 · Region 2 · Set 1 · Q33
(a) 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.
(a)
The sum of the areas of two squares is $\displaystyle 52 \mathrm{~cm}^{2}$ and difference of their perimeters is $\displaystyle 8$ cm . Find the lengths of the sides of the two squares.
OR
(b)
The time taken by a person to travel an upward distance of $\displaystyle 150$ km was $\displaystyle 2 \frac{1}{2}$ hours more than the time taken in the downward return journey. If he returned at a speed of $\displaystyle 10$ km/h more than the speed while going up, find the speeds in each direction.
Marking-scheme solution
Let the lengths of the sides of two squares be 'x' cm and 'y' cm such that \(\displaystyle \mathrm{x}>\mathrm{y}\). ATQ
\[x^{2}+y^{2}=52 \quad \text {--- ① }
\]
\[4 x-4 y=8 \text { or } x-y=2 \quad \text {--- ② }
\]
From ① and ②, we have
\[y^{2}+2 y-24=0
\]
\[\Longrightarrow(y+6)(y-4)=0
\]
\[\therefore y=4
\]
\[\text { So, } x=2+4=6
\]
\(\displaystyle \therefore\) Lengths of the sides of two squares are $\displaystyle 6$ cm and $\displaystyle 4$ cm respectively.
Let the speed in upward direction be 'x' km/h and the speed in downward direction \(\displaystyle =(\mathrm{x}+10) \mathrm{km} / \mathrm{h}\) ATQ
\[\frac{150}{x}-\frac{150}{x+10}=\frac{5}{2}
\]
\[\Rightarrow \mathrm{x}^{2}+10 \mathrm{x}-600=0
\]
\[\Rightarrow(x+30)(x-20)=0
\]
\[\therefore x=20
\]
and \(\displaystyle \mathrm{x}+10=20+10=30\)
Therefore, speeds in upward and downward direction are $\displaystyle 20$ km/h and $\displaystyle 30$ km/h respectively.
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
- 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
- Solve the following system of equations graphically: 2 x+y=5 and 4 x-y=7. Hence, write the coordinates of the points where given lines meet y-axis.2025
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.