All India CA Foundation Group

CI - SI= 110.16
CI= PR^n -1
P(1.06)^3-1
= 0.191016
SI= P×R×N
= P×0.06×3
= 0.18
0.191016-0.18 = 0.011016÷110.16= 10000
therefore, correct option is (d)

1/4-1/6. = 1/12

30.1 is the answer

120

Understanding the Problem
To find the principal amount (p) and the rate of interest (r), we know that:
- Amount after 2 years: A2 = Rs. 5100.5
- Amount after 4 years: A4 = Rs. 5203
Using the formula for compound interest, we can express the amounts as follows:
Amount Formulas
- A2 = p(1 + r/100)²
- A4 = p(1 + r/100)⁴
Setting Up the Equations... more
From the above formulas, we can create two equations:
- Equation 1: p(1 + r/100)² = 5100.5
- Equation 2: p(1 + r/100)⁴ = 5203
Dividing the Equations
To eliminate p, we divide Equation 2 by Equation 1:
- (p(1 + r/100)⁴) / (p(1 + r/100)²) = 5203 / 5100.5
This simplifies to:
- (1 + r/100)² = 5203 / 5100.5
Calculating the Rate
Calculate the right-hand side:
- (1 + r/100)² = 1.01996 (approximately)
Taking the square root gives:
- 1 + r/100 = 1.00995
Thus, r = (1.00995 - 1) * 100 ≈ 0.995%
Finding the Principal
Substituting r back into Equation 1:
- p(1 + 0.00995)² = 5100.5
- p * 1.0199 = 5100.5
Solving for p gives:
- p ≈ 5000
Final Values
- Principal amount, p = Rs. 5000
- Rate of interest, r ≈ 0.995% per annum
This calculation provides both the principal and the interest rate efficiently.

Understanding Offers vs. Invitations to Offer
To determine whether a statement is an offer or an invitation to offer, consider the following factors:
1. Intention of the Parties
- Offers are made with the intention to create a binding contract upon acceptance.
- Invitations to offer indicate a willingness to negotiate or invite offers from others.
2. Clari... morety and Specificity
- Offers generally contain clear and definite terms regarding price, quantity, and other essential elements.
- Invitations to offer are often vague or general, lacking the specificity necessary to form a contract.
3. Communication of Acceptance
- An offer can be accepted to form a contract, while an invitation to offer requires a response in the form of an offer from another party.
- Acceptance is a key factor in distinguishing an offer from an invitation to offer.
4. Context of the Statement
- Analyze the context in which the statement is made (e.g., advertisements, negotiations).
- Advertisements are typically considered invitations to offer, whereas a direct communication with specific terms may be viewed as an offer.
5. Legal Precedents
- Refer to landmark cases such as Carlill v. Carbolic Smoke Ball Co., which illustrates the line between an offer and an invitation to treat.
- Legal interpretations and case law can provide insights into how similar statements have been classified.
Conclusion
Understanding the distinction between an offer and an invitation to offer is crucial in contract law. By evaluating the intention, clarity, communication, context, and legal precedents, one can accurately ascertain the nature of a statement. This evaluation is essential for aspiring legal professionals, particularly in the CA Foundation course.

Understanding the Relationship Between x and y
The equation given is 3x + 4y = 20. This linear equation allows us to express y in terms of x, which helps in understanding how changes in x affect y.
Finding y in terms of x
- Rearranging the equation:
- 4y = 20 - 3x
- y = (20 - 3x) / 4
This indicates that y is a linear function of x.
Quartile Dev... moreiation of x
- The quartile deviation (QD) of x is given as 12.
- QD can be calculated as (Q3 - Q1) / 2, which indicates the spread of the middle 50% of data.
Calculating Quartile Deviation of y
To find the quartile deviation of y, we need to understand how the transformation from x to y affects the dispersion:
- The linear transformation of y = (20 - 3x) / 4 implies that y is influenced by the coefficients of x.
- The transformation has a multiplication factor of -3/4, which affects the spread of the data.
Effect of Transformation on Quartile Deviation
- Since transformations of the form y = mx + c scale the quartile deviation by the absolute value of the coefficient:
- QD(y) = (1/4) * | -3 | * QD(x)
- QD(y) = (3/4) * 12
Calculating QD(y)
- QD(y) = 9
Conclusion
In summary, the quartile deviation of y, derived from the quartile deviation of x through the linear transformation, is 9. This demonstrates how linear relationships impact data spread.

Understanding the Problem
To find the probability of rolling at least one 6 in three throws of a perfect die, we can use the complementary probability method.
Complementary Probability
1. Calculate the probability of NOT rolling a 6:
- The probability of rolling a number other than 6 on a single throw is 5/6.
2. Calculate the probability of NOT rol... moreling a 6 in three throws:
- Since the throws are independent, multiply the probabilities:
- (5/6) x (5/6) x (5/6) = (5/6)^3
3. Calculate (5/6)^3:
- (5/6)^3 = 125/216
Calculating the Required Probability
1. Find the probability of rolling at least one 6:
- Use the complement rule:
- P(at least one 6) = 1 - P(no 6s)
- P(at least one 6) = 1 - (5/6)^3
- P(at least one 6) = 1 - 125/216
2. Final Calculation:
- P(at least one 6) = 216/216 - 125/216
- P(at least one 6) = 91/216
Conclusion
The probability of rolling at least one 6 in three throws of a perfect die is 91/216, which approximates to about 0.4213, or 42.13%.
This means there is a 42.13% chance of getting at least one 6 when throwing a die three times.

Problem Statement
Given two squares with sides p cm and (p + 5) cm, the sum of their squares equals 625 sq. cm. We need to find the values of p.
Step 1: Set Up the Equation
The area of the first square is:
- p²
The area of the second square is:
- (p + 5)²
The equation based on the problem statement is:
- p² + (p + 5)² = 625
Step 2: Expa... morend the Equation
Expanding (p + 5)² gives:
- (p + 5)² = p² + 10p + 25
Now, substitute back into the equation:
- p² + (p² + 10p + 25) = 625
This simplifies to:
- 2p² + 10p + 25 = 625
Step 3: Simplify the Equation
Rearranging gives:
- 2p² + 10p + 25 - 625 = 0
- 2p² + 10p - 600 = 0
Dividing the entire equation by 2 results in:
- p² + 5p - 300 = 0
Step 4: Solve the Quadratic Equation
Using the quadratic formula, p = (-b ± √(b² - 4ac)) / 2a:
- Here, a = 1, b = 5, c = -300
Calculating the discriminant:
- b² - 4ac = 5² - 4(1)(-300) = 25 + 1200 = 1225
Thus, the roots are:
- p = (-5 ± 35) / 2
Calculating the two possible values:
- p = (30 / 2) = 15 (positive root)
- p = (-40 / 2) = -20 (not valid as side length cannot be negative)
Step 5: Final Answer
The side lengths of the squares are:
- First square: 15 cm
- Second square: 20 cm (15 + 5)