Reena has pend and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, the number of pencils would become 4 times the number of pens. Find the original number of pens and pencils.
Given:
(i) Total numbers of pens and pencils = 40.
(ii) If she has 5 more pencil and 5 less pens, the number of pencils would be 4 times the number of pen.
To find: Original number of pens and pencils.
Suppose original number of pencil = x
And original number of pen = y
According the given conditions, we have,
$x+y=40$
$x+y-40=0$...(1)
$5+x=4(y-5)$
$5+x=4 y-20$
$x-4 y+5+20=0$
$x-4 y+25=0$....(2)
Thus we got the following system of linear equations
$x+y-40=0$$\ldots \ldots(1)$
$x-4 y+25=0$$\ldots \ldots(2)$
Substituting the value of y from equation 1 in equation 2 we get
$x-4(40-x)+25=0 \quad[y=(40-x)$ from equation 1$]$
$x-160+4 x+25=0$
$5 x-135=0$
$x=\frac{135}{5}$
$x=27$
Substituting the value of y in equation 1 we get
$27+y=40$
$y=40-27$
$y=13$
Hence we got the result number of pencils is $x=27$ and number of pens are $y=13$
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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,