✓ Board-verified
Mathematics · 2025 · 5 marks
CBSE 2025 · Region 1 · Set 2 · Q35
(a) A two-digit number is such that the product of its digits is 12. When 36 is added to this number, the digits interchange their places. Find the…
(a)
A two-digit number is such that the product of its digits is 12. When $\displaystyle 36$ is added to this number, the digits interchange their places. Find the number.
OR
(b)
A student scored a total of $\displaystyle 32$ marks in class tests in Mathematics and Science. Had he scored $\displaystyle 2$ marks less in Science and $\displaystyle 4$ marks more in Mathematics, the product of his marks would have been 253. Find his marks in the two subjects.
Marking-scheme solution
Let unit digit be y and ten's digit \(\displaystyle =x\)
hence, the two digit number \(\displaystyle =10 \mathrm{x}+\mathrm{y}\),
ATQ
\[x y=12 \quad \ldots \ldots \text { (i) }
\]
\(\displaystyle 10 x+y+36=10 y+x\)
\[x-y+4=0 \quad \ldots \ldots \text { (ii) }
\]
From (i) and (ii)
\[\begin{aligned}
& x^{2}+4 x-12=0 \\
& (x+6)(x-2)=0
\end{aligned}
\]
Hence, \(\displaystyle x=2\)
\[\text { and } y=6
\]
∴ Number = $\displaystyle 26$
Let marks scored in Mathematics be \(\displaystyle x\) and marks scored in Science be \(\displaystyle y\)
ATQ,
\[x+y=32 \quad \ldots \ldots \text { (i) }
\]
\[\text { and }(x+4)(y-2)=253 \quad \ldots \ldots \text { (ii) }
\]
from (i) and (ii)
\[x^{2}-26 x+133=0
\]
\[(x-19)(x-7)=0
\]
\(\displaystyle x=19,7\)
\[\left.\begin{array}{l}
x=19 \Rightarrow y=13 \\
x=7 \Rightarrow y=25
\end{array}\right\}
\]
Hence, marks in Mathematics and Science are $\displaystyle 19$, $\displaystyle 13$ or $\displaystyle 7$, $\displaystyle 25$
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.