✓ Board-verified
Mathematics · 2025 · 5 marks
CBSE 2025 · Region 2 · Set 3 · Q35
(a) The numerator of a fraction is 3 less than its denominator. If 2 is added to both numerator and denominator, then the sum of the new fraction and…
(a)
The numerator of a fraction is $\displaystyle 3$ less than its denominator. If $\displaystyle 2$ is added to both numerator and denominator, then the sum of the new fraction and the original fraction is $\displaystyle 1 \frac{9}{20}$. Find the original fraction.
OR
(b)
A train travelling at a uniform speed for $\displaystyle 360$ km would have taken $\displaystyle 48$ minutes less to travel the same distance if its speed were $\displaystyle 5$ km/h more. Find the original speed of the train.
Marking-scheme solution
Let denominator be x
∴ Numerator \(\displaystyle =(\mathrm{x}-3)\)
Therefore, fraction \(\displaystyle =\frac{\mathrm{x}-3}{\mathrm{x}}\)
ATQ
\[\frac{x-3}{x}+\frac{x-3+2}{x+2}=\frac{29}{20}
\]
\(\displaystyle \Rightarrow 11 \mathrm{x}^{2}-98 \mathrm{x}-120=0\)
\(\displaystyle \Rightarrow(\mathrm{x}-10)(11 \mathrm{x}+12)=0\)
So, \(\displaystyle \mathrm{x}=10\)
∴ Fraction \(\displaystyle =\frac{7}{10}\)
Let the original speed of train be 'x' km/h ATQ
\[\frac{360}{x}-\frac{360}{x+5}=\frac{48}{60}
\]
\[\begin{aligned}
& \Rightarrow x^{2}+5 x-2250=0 \\
& \Rightarrow(x+50)(x-45)=0
\end{aligned}
\]
So, \(\displaystyle \mathrm{x}=45\)
∴ Original speed of the train is $\displaystyle 45$ km/h.
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.