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When the rate of simple interest is different for different years, a sum of Rs. X becomes 108% of itself in 1 year and 130% of itself in 3 years. If the interest obtained in the first, second and third years are in A.P., what is the ratio of the amount of interest obtained in the first year and in the third year, respectively?
  • a)
    2 : 3
  • b)
    3 : 4
  • c)
    1 : 2
  • d)
    5 : 8
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
When the rate of simple interest is different for different years, a s...
Given data:
- Amount after 1 year = 108% of X
- Amount after 3 years = 130% of X
- Interest obtained in the first, second, and third years are in A.P.

Solution:

Let the principal amount be Rs. X

Amount after 1 year:
- Principal + Interest for the first year = 108% of X
- Principal + (Principal * Rate for the first year) = 108/100 * X
- Principal(1 + Rate for the first year) = 1.08X

Amount after 3 years:
- Principal + Interest for 3 years = 130% of X
- Principal + (Principal * Rate for 3 years) = 130/100 * X
- Principal(1 + 3 * Rate for the first year) = 1.3X

Interest obtained in the first year:
- Interest for the first year = 1.08X - X = 0.08X

Interest obtained in the second year:
- Let the interest obtained in the second year be Y
- Interest for the second year = 1.3X - 1.08X = 0.22X
- Y - 0.08X = 0.22X - 0.08X
- Y = 0.14X

Interest obtained in the third year:
- Interest for the third year = 1.3X - (1.08X + Y) = 1.3X - (1.08X + 0.14X) = 0.08X

Ratio of interest obtained in the first year and the third year:
- 0.08X : 0.08X = 1 : 1
- Therefore, the ratio of the amount of interest obtained in the first year and in the third year is 1 : 1, which simplifies to 1 : 1 or 1 : 1.
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Community Answer
When the rate of simple interest is different for different years, a s...
Let the principal = 100x
First year interest = 108% (100x) – 100x = 8x
Interest in three years = 130% (100x) – 100x = 30x
As the successive interest in the years is in A.P.

Interest in third year = 30x – (10x + 8x) = 12x
Reqd. ratio = 8 : 12 = 2 : 3
Hence, option A is correct.
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When the rate of simple interest is different for different years, a sum of Rs. X becomes 108% of itself in 1 year and 130% of itself in 3 years. If the interest obtained in the first, second and third years are in A.P., what is the ratio of the amount of interest obtained in the first year and in the third year, respectively?a)2 : 3b)3 : 4c)1 : 2d)5 : 8Correct answer is option 'A'. Can you explain this answer?
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When the rate of simple interest is different for different years, a sum of Rs. X becomes 108% of itself in 1 year and 130% of itself in 3 years. If the interest obtained in the first, second and third years are in A.P., what is the ratio of the amount of interest obtained in the first year and in the third year, respectively?a)2 : 3b)3 : 4c)1 : 2d)5 : 8Correct answer is option 'A'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about When the rate of simple interest is different for different years, a sum of Rs. X becomes 108% of itself in 1 year and 130% of itself in 3 years. If the interest obtained in the first, second and third years are in A.P., what is the ratio of the amount of interest obtained in the first year and in the third year, respectively?a)2 : 3b)3 : 4c)1 : 2d)5 : 8Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When the rate of simple interest is different for different years, a sum of Rs. X becomes 108% of itself in 1 year and 130% of itself in 3 years. If the interest obtained in the first, second and third years are in A.P., what is the ratio of the amount of interest obtained in the first year and in the third year, respectively?a)2 : 3b)3 : 4c)1 : 2d)5 : 8Correct answer is option 'A'. Can you explain this answer?.
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