In a potato race 20 potatoes are placed in a line at intervals of 4 metres with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
Given at start he has to run 24m to get the first potato then 28 m as the next potato is 4m away from first and so on
Hence the sequence of his running will be 24, 28, 32 …
There are 20 terms in sequence as there are 20 potatoes
Hence only to get potatoes from starting point he has to run
24 + 28 + 32 + … up to 20 terms
This is only from starting point to potato but he has to get the potato back to starting point hence the total distance will be twice that is
Total distance ran = 2 × (24 + 28 + 32…) … 1
Let us find the sum using he formula to find sum of n terms of AP
That is Sn = n/2 (2a + (n – 1) d)
There are 20 terms hence n = 20
⇒ S20 = (20/2) (2 (24) + (20 – 1) 4)
On simplification we get
⇒ S20 = 10(48 + 19(4))
⇒ S20 = 10(48 + 76)
On computing we get
⇒ S20 = 10 × 124
⇒ S20 = 1240 m
Using equation 1
⇒ Total distance ran = 2 × 1240
⇒ Total distance ran = 2480 m
Hence total distance he has to run is 2480 m
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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,