Liza deposits money in her savings bank in such a way that every next day her deposit amount is 12 more than her previous day deposit. If she starts her deposit with 12 on the first day, the total amount deposited by Liza at the end of 30 days will be || ADRE 1.0 SLRC 2022 PAPER-III SOLVED QUESTIONS
Liza deposits money in her savings bank in such a way that every next day her deposit amount is ₹12 more than her previous day deposit. If she starts her deposit with ₹12 on the first day, the total amount deposited by Liza at the end of 30 days will be:
(A) ₹5,420
(B) ₹5,580
(C) ₹5,620
(D) ₹5,780
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Solution:
To solve this problem, we need to determine the total amount of money Liza deposits over 30 days, where each day's deposit is ₹12 more than the previous day's deposit.
Let's define the amount Liza deposits on the n-th day as an.
Given:
- The deposit on the first day a1 = ₹12.
- Each subsequent day's deposit is ₹12 more than the previous day: an+1 = an + ₹12.
This forms an arithmetic sequence where:
- The first term a1 = ₹12.
- The common difference d = ₹12.
The n-th term of an arithmetic sequence can be calculated using the formula:
an = a1 + (n-1)d
To find the total amount deposited by Liza over 30 days, we need the sum of the first 30 terms of this arithmetic sequence. The sum Sn of the first n terms of an arithmetic sequence is given by:
Sn = n/2 × (2a1 + (n-1)d)
For n = 30:
S30 = 30/2 × (2 × ₹12 + (30-1) × ₹12)
Simplify the expression inside the parentheses:
S30 = 15 × (24 + 29 × ₹12)
Calculate 29 × ₹12:
29 × ₹12 = ₹348
Now add 24 to 348:
24 + 348 = ₹372
Finally, multiply by 15:
S30 = 15 × ₹372 = ₹5580
Therefore, the total amount deposited by Liza at the end of 30 days is ₹5580.
The correct answer is:
(B) ₹5580
Importance of the Question
- Exam Relevance: This question was part of the ADRE SLRC-2022 Paper III, which makes it a valuable reference for understanding the type of arithmetic problems that can appear in the exam.
- Concept Application: It tests the understanding of arithmetic sequences, a fundamental topic in mathematics, which is crucial for many competitive exams.
- Problem-Solving Skills: Solving this problem enhances problem-solving abilities and helps in improving speed and accuracy in calculations.
- Pattern Recognition: Recognizing and working with patterns, like arithmetic progressions, is a critical skill in various mathematical contexts.
- Practice for Similar Exams: Preparing with questions from previous years’ papers helps in familiarizing with the exam pattern and difficulty level, thus aiding in better preparation for similar competitive exams.
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