MAH MCA CET 2025
The population of a town grows at the rate of 10% per year. How long will it take for the population to triple?
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option B —
Detailed Solution
Growth at the rate of 10% per year means .
Solving, .
For the population to triple, , so years, where is the natural logarithm (about 11 years).
✓ Check
years; compounding once a year instead gives years, a similar size.⚠ Common trap
Option (C), years, divides by the rate instead of multiplying. The source key gave (C), which is wrong.Quick tip
to multiply by
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Differential Equations — Preparation
This question tests your understanding of Differential Equations, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
A differential equation is an equation involving a function and its derivatives. This topic covers the order and degree of a differential equation, forming a differential equation by eliminating arbitrary constants, and solving first-order equations. The main solution methods are variables separable, homogeneous equations (using the substitution y = vx), and linear equations of the form dy/dx + Py = Q, solved with the integrating factor e^(integral of P dx). Exam questions also include application problems on growth and decay, such as population growth, radioactive decay and Newton's law of cooling. Remember that the degree is defined only when the equation is a polynomial in its derivatives. Practise the differential equations questions below, each with a step-by-step solution.