RRB Group D Maths Simple Interest By Manoj Sir

Simple Interest (SI) is a fundamental concept in mathematics, vital for competitive exams like RRB Group D. It represents the interest calculated only on the initial sum of money, or principal. Unlike compound interest, the principal amount remains constant throughout the loan or investment period, making its calculation straightforward. Mastering SI is essential for financial aptitude and problem-solving.

Also Read: RRB Group D Maths Syllabus

Introduction to Simple Interest

Simple Interest (SI) is calculated on the principal amount. The core formula for calculating Simple Interest is:

SI = (P × R × T) / 100

Where:

• SI = Simple Interest (साधारण ब्याज)

• P or PA = Principal (मूलधन): The initial sum of money. The principal is always considered 100% of itself.

• R = Rate (दर): The annual interest rate.

• T = Time (समय): The duration for which the money is borrowed or lent, in years.

• AMT = Amount (मिश्रधन): The total sum after adding the interest to the principal (Amount = Principal + SI).

A key characteristic of simple interest is that interest is not charged on the interest itself; the principal amount does not change over the period.

Deriving Formulas for Rate, Principal, and Time

The main formula can be rearranged to directly solve for Rate, Principal, or Time. By cross-multiplying the base formula SI = (P × R × T) / 100, we get SI × 100 = P × R × T.

From this, the following direct formulas are derived:

• To find the Rate (R):
  R = (SI × 100) / (P × T)

• To find the Principal (P):
  P = (SI × 100) / (R × T)

• To find the Time (T):
  T = (SI × 100) / (P × R)

Relationship Between SI, Rate, and Time

When the principal is held constant, Simple Interest is directly proportional to the product of the rate and time. This offers a powerful shortcut:

Simple Interest (as a percentage) = Rate × Time

For instance, if the rate is 4% per year for 3 years, the total simple interest will be 4% × 3 = 12% of the principal.

Problem Type 1: Ratio and Fractional Relationships

These problems provide the relationship between Principal and Simple Interest as a ratio or a fraction.

(Memory Tip: When a problem states "Simple interest is a fraction of the principal" (साधारण ब्याज मूलधन का…), the denominator of the fraction represents the Principal, and the numerator represents the Simple Interest.)

Consider an example: For 5 years, the simple interest on a sum is 1/4 of the sum (principal). To find the annual rate of interest:

Here, SI = 1, P = 4, and T = 5 years.

Using the formula R = (SI × 100) / (P × T):

R = (1 × 100) / (4 × 5) = 100 / 20 = 5%.

Problem Type 2: Rate and Time are Numerically Equal

This is a special case where the value of the annual rate percentage is equal to the number of years (i.e., R = T).

Special Formula / Shortcut:

When Rate and Time are equal, the rate (or time) can be found using:

Rate (or Time) = √(SI / P) × 10

For example: The simple interest on a sum is 16/25 of the principal. The rate percent and time in years are numerically equal. To find the rate of interest:

Here, SI/P = 16/25.

Rate = √(16 / 25) × 10 = (4 / 5) × 10 = 8%.

Problem Type 3: "Times" (गुणा) Problems

These problems describe a principal amount becoming 'n' times itself over a certain period or at a certain rate.

Core Formula for "Times" Problems:

The formula relates the number of times (n), rate (R), and time (T). Always subtract 1 from the number of times (n).

• If you need to find the Rate:
  R = [(n - 1) / T] × 100

• If you need to find the Time:
  T = [(n - 1) / R] × 100

Where n is the number of times the principal has become.

Example: A sum of money becomes 6 times itself in 20 years. To find the rate of interest:

Given, n = 6, T = 20 years.

R = [(6 - 1) / 20] × 100 = (5 / 20) × 100 = (1/4) × 100 = 25%.

Problem Type 4: Two "Times" Conditions

These problems involve two scenarios where a sum becomes 'n' times itself.

Direct Proportionality Shortcut:

1. For the first condition, note the given rate/time and calculate n₁ - 1.

2. For the second condition, note the unknown rate/time and calculate n₂ - 1.

3. Find the multiplicative relationship between (n₁ - 1) and (n₂ - 1) and apply it to the corresponding rate/time.

Example: A sum becomes 4 times itself at 5% p.a. At what rate will it become 7 times itself?

• Condition 1: 5% rate corresponds to 4 - 1 = 3.

• Condition 2: Unknown rate corresponds to 7 - 1 = 6.

To get from 3 to 6, multiply by 2. Apply this to the rate: 5% × 2 = 10%. The new rate is 10%.

Problem Type 5: Change in Interest Rate

These problems involve a change in the interest rate, leading to a corresponding change in the total simple interest received. The principal is assumed to be constant.

Logic:

Use the direct relationship: Total Interest Change = Total Rate Change × Time

Example: A sum is lent for 3 years. If the rate had been 4% lower, the interest received would have been ₹720 less. To find the principal:

The annual rate reduction is 4%. Over 3 years, the total rate reduction is 4% × 3 = 12%.

This 12% reduction in interest corresponds to ₹720.

If 12% of Principal = ₹720, then 1% of Principal = ₹720 / 12 = ₹60.

Therefore, 100% of Principal = ₹60 × 100 = ₹6,000.