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Arjun invested Rs. ‘a’ and Rs. (a + 800) in schemes X and Y respectively. Scheme X offering compound interest of 20% p.a. compounded annually and scheme Y offering simple interest of 15% p.a. If at the end of 2nd year, difference of the interest received from both schemes were Rs. 12, then find the value of ‘a’ such that ‘a’ is an integral value?
- a)Rs.2400
- b)Rs.1800
- c)Rs.2800
- d)Rs.1600
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Arjun invested Rs. ‘a’ and Rs. (a + 800) in schemes X and Y respectiv...
According to the question,
Case I:
[a × 1.2 × 1.2 – a] – [(a + 800) × 0.15 × 2] = 12
0.44a – 0.3a – 240 = 12
0.14a = 252
a = 1800
Case II:
[(a + 800) × 0.15 × 2] – [a × 1.2 × 1.2 – a] = 12
0.3a + 240 – 0.44a = 12
228 = 0.14a
a = 1628.57 (not possible)
Hence, the value of a is Rs. 1800
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Arjun invested Rs. ‘a’ and Rs. (a + 800) in schemes X and Y respectiv...
To find the value of 'a' that satisfies the given conditions, let's analyze the interest earned on each scheme separately.
Scheme X:
Compound interest is calculated using the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In Scheme X, the principal amount is 'a' and the interest rate is 20% (or 0.2). The interest is compounded annually, so n = 1. After 2 years, the final amount from Scheme X would be:
A1 = a(1 + 0.2/1)^(1*2)
A1 = a(1.2)^2
A1 = 1.44a
Scheme Y:
Simple interest is calculated using the formula:
I = P * r * t
Where:
I = the interest earned
P = the principal amount
r = the annual interest rate (as a decimal)
t = the number of years
In Scheme Y, the principal amount is Rs. (a + 800) and the interest rate is 15% (or 0.15). After 2 years, the interest earned from Scheme Y would be:
I2 = (a + 800) * 0.15 * 2
I2 = 0.3(a + 800)
Difference of Interest:
The difference in interest earned between Scheme X and Scheme Y after 2 years is given as Rs. 12. So we can write the equation:
A1 - I2 = 12
Substituting the values of A1 and I2:
1.44a - 0.3(a + 800) = 12
1.44a - 0.3a - 240 = 12
1.14a - 240 = 12
1.14a = 252
a = 252 / 1.14
a ≈ 2210.53
Since 'a' needs to be an integral value, the closest integral value to 2210.53 is 2211. Therefore, the value of 'a' that satisfies the given conditions is Rs. 2211.
However, none of the options provided match the value of 'a' calculated. Therefore, the correct answer cannot be determined from the given options.
Scheme X:
Compound interest is calculated using the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In Scheme X, the principal amount is 'a' and the interest rate is 20% (or 0.2). The interest is compounded annually, so n = 1. After 2 years, the final amount from Scheme X would be:
A1 = a(1 + 0.2/1)^(1*2)
A1 = a(1.2)^2
A1 = 1.44a
Scheme Y:
Simple interest is calculated using the formula:
I = P * r * t
Where:
I = the interest earned
P = the principal amount
r = the annual interest rate (as a decimal)
t = the number of years
In Scheme Y, the principal amount is Rs. (a + 800) and the interest rate is 15% (or 0.15). After 2 years, the interest earned from Scheme Y would be:
I2 = (a + 800) * 0.15 * 2
I2 = 0.3(a + 800)
Difference of Interest:
The difference in interest earned between Scheme X and Scheme Y after 2 years is given as Rs. 12. So we can write the equation:
A1 - I2 = 12
Substituting the values of A1 and I2:
1.44a - 0.3(a + 800) = 12
1.44a - 0.3a - 240 = 12
1.14a - 240 = 12
1.14a = 252
a = 252 / 1.14
a ≈ 2210.53
Since 'a' needs to be an integral value, the closest integral value to 2210.53 is 2211. Therefore, the value of 'a' that satisfies the given conditions is Rs. 2211.
However, none of the options provided match the value of 'a' calculated. Therefore, the correct answer cannot be determined from the given options.
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Arjun invested Rs. ‘a’ and Rs. (a + 800) in schemes X and Y respectively. Scheme X offering compound interest of 20% p.a. compounded annually and scheme Y offering simple interest of 15% p.a. If at the end of 2nd year, difference of the interest received from both schemes were Rs. 12, then find the value of ‘a’ such that ‘a’ is an integral value?a)Rs.2400b)Rs.1800c)Rs.2800d)Rs.1600e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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Arjun invested Rs. ‘a’ and Rs. (a + 800) in schemes X and Y respectively. Scheme X offering compound interest of 20% p.a. compounded annually and scheme Y offering simple interest of 15% p.a. If at the end of 2nd year, difference of the interest received from both schemes were Rs. 12, then find the value of ‘a’ such that ‘a’ is an integral value?a)Rs.2400b)Rs.1800c)Rs.2800d)Rs.1600e)None of theseCorrect answer is option 'B'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Arjun invested Rs. ‘a’ and Rs. (a + 800) in schemes X and Y respectively. Scheme X offering compound interest of 20% p.a. compounded annually and scheme Y offering simple interest of 15% p.a. If at the end of 2nd year, difference of the interest received from both schemes were Rs. 12, then find the value of ‘a’ such that ‘a’ is an integral value?a)Rs.2400b)Rs.1800c)Rs.2800d)Rs.1600e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Arjun invested Rs. ‘a’ and Rs. (a + 800) in schemes X and Y respectively. Scheme X offering compound interest of 20% p.a. compounded annually and scheme Y offering simple interest of 15% p.a. If at the end of 2nd year, difference of the interest received from both schemes were Rs. 12, then find the value of ‘a’ such that ‘a’ is an integral value?a)Rs.2400b)Rs.1800c)Rs.2800d)Rs.1600e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Arjun invested Rs. ‘a’ and Rs. (a + 800) in schemes X and Y respectively. Scheme X offering compound interest of 20% p.a. compounded annually and scheme Y offering simple interest of 15% p.a. If at the end of 2nd year, difference of the interest received from both schemes were Rs. 12, then find the value of ‘a’ such that ‘a’ is an integral value?a)Rs.2400b)Rs.1800c)Rs.2800d)Rs.1600e)None of theseCorrect answer is option 'B'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Arjun invested Rs. ‘a’ and Rs. (a + 800) in schemes X and Y respectively. Scheme X offering compound interest of 20% p.a. compounded annually and scheme Y offering simple interest of 15% p.a. If at the end of 2nd year, difference of the interest received from both schemes were Rs. 12, then find the value of ‘a’ such that ‘a’ is an integral value?a)Rs.2400b)Rs.1800c)Rs.2800d)Rs.1600e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Arjun invested Rs. ‘a’ and Rs. (a + 800) in schemes X and Y respectively. Scheme X offering compound interest of 20% p.a. compounded annually and scheme Y offering simple interest of 15% p.a. If at the end of 2nd year, difference of the interest received from both schemes were Rs. 12, then find the value of ‘a’ such that ‘a’ is an integral value?a)Rs.2400b)Rs.1800c)Rs.2800d)Rs.1600e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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