Mathematical Aptitude
Mathematical aptitude requires the swift application of foundational arithmetic formulas. This section codifies the essential theorems and equations necessary for solving Time & Distance, Profit & Loss, and Interest problems in the UGC NET examination.
1. Time and Distance
The fundamental relationship governing motion is:
\( \text{Distance} = \text{Speed} \times \text{Time} \)
💡 Conversion Shortcut
To convert km/hr to m/s, multiply by \( \frac{5}{18} \).
To convert m/s to km/hr, multiply by \( \frac{18}{5} \).
Average Speed: If a certain distance is covered at speed \(x\) and the same distance is covered at speed \(y\), the average speed for the whole journey is:
\( \text{Average Speed} = \frac{2xy}{x + y} \)
2. Profit and Loss
Let Cost Price be \(CP\) and Selling Price be \(SP\).
- Gain (Profit): \( SP - CP \) (where \(SP > CP\))
- Loss: \( CP - SP \) (where \(CP > SP\))
Percentages are always calculated on the Cost Price (unless otherwise specified):
\( \text{Gain } \% = \left( \frac{\text{Gain}}{CP} \right) \times 100 \)
\( \text{Loss } \% = \left( \frac{\text{Loss}}{CP} \right) \times 100 \)
3. Simple and Compound Interest
Let Principal = \(P\), Rate = \(R\%\) per annum, and Time = \(T\) years.
Simple Interest (SI)
Interest is calculated only on the initial principal amount.
\( SI = \frac{P \times R \times T}{100} \)
\( \text{Total Amount} = P + SI \)
Compound Interest (CI)
Interest is calculated on the initial principal and also on the accumulated interest of previous periods.
\( \text{Amount (A)} = P \left(1 + \frac{R}{100}\right)^T \)
\( CI = A - P \)
Note: If interest is compounded half-yearly, the rate becomes \(R/2\) and time becomes \(2T\).
4. Averages
The average (or arithmetic mean) of a set of data is the sum of the quantities divided by the number of quantities.
\( \text{Average} = \frac{\text{Sum of all observations}}{\text{Total number of observations}} \)
If the average of \(n_1\) quantities is \(a_1\), and the average of \(n_2\) quantities is \(a_2\), then the weighted average of all quantities is:
\( \text{Weighted Average} = \frac{n_1a_1 + n_2a_2}{n_1 + n_2} \)
Academic References
- Aggarwal, R. S. (2018). Quantitative aptitude for competitive examinations. S. Chand Publishing.
- Madaan, K. V. (2023). UGC NET/SET/JRF General Paper-1: Teaching and Research Aptitude (7th ed.). Pearson India.