A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?
Given the total amount saved in 20 years is 66000 hence S20 = 66000
Let the amount saved in first year be ‘a’
Then as he increases 200 Rs every year then the amount in second year will be ‘a + 200’ then in third year ‘a + 400’ and so on
The sequence will be a, a + 200, a + 400…
The sequence is AP and the common difference is d = 200
There are 20 terms in the sequence as he saved money for 20 years
Using the sum formula for AP Sn = n/2 (2a + (n – 1) d) we get
Where n is number of terms a is the first term and d is the common difference
Given that S20 = 66000
S20 = (20/2) (2a + (20 – 1) 200)
⇒ 66000 = 10(2a + 19 × 200)
⇒ 6600 = 2a + 3800
⇒ 6600 – 3800 = 2a
⇒ 2a = 2800
⇒ a = 1400
Hence amount saved in first year is 1400 Rs.
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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,