A number consist of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.
Let the digits at units and tens place of the given number be $x$ and $y$ respectively. Thus, the number is $10 y+x$.
The sum of the digits of the number is 5 . Thus, we have $x+y=5$
After interchanging the digits, the number becomes $10 x+y$.
The number obtained by interchanging the digits is greater by 9 from the original number. Thus, we have
$10 x+y=10 y+x+9$
$\Rightarrow 10 x+y-10 y-x=9$
$\Rightarrow 9 x-9 y=9$
$\Rightarrow 9(x-y)=9$
$\Rightarrow x-y=\frac{9}{9}$
$\Rightarrow x-y=1$
So, we have two equations
$x+y=5$
$x-y=1$
Here x and y are unknowns. We have to solve the above equations for x and y.
Adding the two equations, we have
$(x+y)+(x-y)=5+1$
$\Rightarrow x+y+x-y=6$
$\Rightarrow 2 x=6$
$\Rightarrow x=\frac{6}{2}$
$\Rightarrow x=3$
Substituting the value of x in the first equation, we have
$3+y=5$
$\Rightarrow y=5-3$
$\Rightarrow y=2$
Hence, the number is $10 \times 2+3=23$.
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,