SSC CGL Maths Arithmetic SI & CI by Ravinder Sir

SSC CGL Maths Arithmetic includes many important topics, and Simple Interest and Compound Interest are among them. These topics are useful because questions from SI and CI are often asked in different forms. Students may get direct formula-based questions, percentage-based questions, ratio-based questions, or mixed questions where both SI and CI concepts are used together.

Simple Interest and Compound Interest are not difficult when students understand the basic concepts clearly. Many students try to solve these questions by using long methods. However, these questions can be solved faster when the basic formulas, percentage method, ratio method, and comparison method are clear.

For SSC CGL preparation, students should focus on concept clarity first. After that, they should practise different types of questions regularly. SI and CI questions can be solved with accuracy when students understand how principal, rate, time, interest, and amount are connected.

Also Read: 

• SSC CGL Maths Arithmetic Profit and Loss
• SSC CGL Quantitative Aptitude Syllabus

What is Simple Interest?

Simple Interest is the interest calculated only on the principal amount. The interest remains the same every year because it is not added back to the principal.

The basic formula of Simple Interest is: 

Simple Interest = Principal × Rate × Time / 100

Here:

• Principal means the amount invested or borrowed.

• Rate means the rate of interest per year.

• Time means the duration for which the money is invested or borrowed.

• Amount means the total money received or paid after adding interest.

Amount = Principal + Simple Interest

Simple Interest = Amount - Principal

These formulas are the base of almost every SI question. Students should remember them clearly before moving to advanced questions.

Simple Interest Through Percentage Method

This method makes calculations faster.

Example: Rate = 10%, Time = 4 years

• SI = 10% × 4 = 40%

• Principal = 100%

• Amount = 100% + 40% = 140%

Example: Rate = 20%, Time = 3 years

• SI = 20% × 3 = 60%

• Principal = 100%

• Amount = 100% + 60% = 160%

Direct Questions on Simple Interest

Some SI questions are direct and can be solved in a few seconds.

For example, if ₹4,000 is invested at 15% per annum for 5 years, then the Simple Interest will be:

• 15% × 5 = 75%

• 75% of ₹4,000 = ₹3,000

• So, the Simple Interest is ₹3,000.

This type of question checks basic percentage understanding. Students should practise percentage conversions such as 75% = 3/4, 25% = 1/4, and 50% = 1/2.

Change in Time and Simple Interest

Simple Interest is directly proportional to principal, rate, and time. If any one of these changes, the interest also changes.

For example, if the Simple Interest on ₹625 increases by ₹25 when time increases by 2 years, then the rate can be found by using the change in interest.

• Here, extra interest = ₹25

• Principal = ₹625

• Extra time = 2 years

• Rate = 25 × 100 / 625 × 2

• Rate = 2%

This type of question is common in SSC exams. Students should understand that change in interest happens because of change in time, principal, or rate.

When Simple Interest is Given as a Fraction of Principal

Sometimes, Simple Interest is given as a fraction of the principal. These questions are also simple if the formula is used properly.

For example, if Simple Interest is 4/9 of the principal and rate is equal to time, then:

• SI = 4P/9

• SI = P × R × T / 100

• Since R = T,

• 4P/9 = P × R × R / 100

• P gets cancelled.

• 4/9 = R² / 100

• R² = 400/9

• R = 20/3

• So, rate = 6 2/3%

This type of question requires careful equation formation. Students should avoid guessing in such questions.

When Money Becomes Double or Triple

Many SSC CGL questions ask when a sum becomes double or triple at Simple Interest. If a sum becomes three times, it means:

• Principal = 1 unit

• Amount = 3 units

• Interest = 2 units

If it becomes three times in 20 years, then 2 units of interest are earned in 20 years. So, 1 unit of interest will be earned in 10 years. Hence, the sum will become double in 10 years.

This method is very fast and avoids long calculations.

Similarly, if a sum becomes double in 5 years, then it earns interest equal to the principal in 5 years. So, the rate will be 20% per annum.

What is Compound Interest?

Compound Interest is different from Simple Interest. In Compound Interest, interest is calculated on the principal and also on the interest already added. This means interest increases every year because the amount keeps increasing.

The basic formula of Compound Interest is: Amount = Principal × (1 + R/100)^T

• Compound Interest = Amount - Principal

• Here, R is the rate of interest and T is the time period.

Compound Interest questions in SSC CGL can be solved through different methods. These include formula method, percentage method, ratio method, golden ratio method, and tree method.

Method 1: Percentage (Successive) Method

This method uses the concept of successive percentage change.

Example: Rate = 8%, Time = 2 years

• SI for 2 years = 8% + 8% = 16%

• Extra interest in CI = 8% of 8% = 0.64%

• CI for 2 years = 16.64%

Method 2: Ratio Method

Convert the rate into a fraction and use it to find the ratio of Principal to Amount.

Example: Rate = 10%, Time = 2 years

• 10% = 1/10, so for every ₹10 principal, ₹1 interest is earned.

• After Year 1: P = 10, Amount = 11

• After Year 2: P = 11, Amount = 11 × (11/10)

• Principal : Amount = 100 : 121

Method 3: Formula Method

Amount = P × (1 + R/100)^T

From this formula:

• Amount / Principal = (1 + R/100)^T

• If T = 2, the relationship involves a square root.

• If T = 3, the relationship involves a cube root.

• The power in the formula is always equal to the time period.

Method 4: Golden Ratio

The Golden Ratio helps solve certain types of CI questions quickly.

How to remember: Start with the number of years. Add adjacent terms to get the next row. The last term is always 1.

Method 5: Tree Method

This method is useful for 2-year and 3-year problems.

For 2 years:

• Year 1 interest on P = A

• Year 2 interest on P = A

• Interest on Year 1 interest = B (called the extra CI interest)

• CI − SI for 2 years = B

For 3 years:

• Each of the two "A" values earns interest B.

• B earns its own interest C.

• CI − SI for 3 years = 2B + C

Important Solved Examples

Below are some solved examples for the understanding of the students

Example 1

Find the SI on ₹4,000 at 15% per annum for 5 years.

• SI = 15% × 5 = 75% of ₹4,000

• 75% = 3/4

• SI = ₹3,000

Example 2

A sum becomes 3 times in 20 years at SI. In how many years will it become double?

• 1 → 3 means an increase of 2 units in 20 years.

• 1 unit = 10 years.

• For doubling: 1 → 2 means an increase of 1 unit.

• Time = 10 years

Example 3

A sum doubles at 5% and amounts to ₹150. The same sum amounts to ₹100 at 3%. Find the principal.

• Difference in rate = 2%, Difference in amount = ₹50

• 1% change = ₹25 interest

• At 3%: Interest = ₹75

• Principal = Amount − Interest = ₹100 − ₹75 = ₹25

Example 4

A person invests in three schemes for 6, 10, and 12 years at 10%, 12%, and 15% respectively. He gets equal interest from all three. Find the ratio of investments.

• Scheme 1 SI% = 6 × 10 = 60%

• Scheme 2 SI% = 10 × 12 = 120%

• Scheme 3 SI% = 12 × 15 = 180%

Since SI is equal in all three:

• P1 × 60 = P2 × 120 = P3 × 180

• Ratio = 1/60 : 1/120 : 1/180 = 6 : 3 : 2

Tips for the Exam

1. Always treat the Principal as 100% when using the percentage method.

2. Simple Interest does not change from year to year. Use this to set up direct equations.

3. When the time period and rate are equal in a CI problem, use the formula method with powers.

4. The difference between CI and SI for 2 years = P × (R/100)²

5. The difference between CI and SI for 3 years = P × (R/100)² × (3 + R/100)

6. Practice converting rates to fractions for the ratio method. For example, 10% = 1/10, 20% = 1/5, 25% = 1/4.

SSC CGL Maths Arithmetic SI and CI is an important part of quantitative aptitude preparation. Simple Interest questions are based on principal, rate, time, interest, and amount. Compound Interest questions require understanding of increasing interest, effective percentage, ratio method, formula method, and difference between SI and CI.