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Vishal deposited Rs. X at 10% p.a. compound interest for 2 years and Rs. Y at 20% p.a. compound interest for 2 years. If his overall interest is 35% of the overall amount, what is X : Y?
- a)1 : 3
- b)9 : 14
- c)11 : 15
- d)12 : 17
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Vishal deposited Rs. X at 10% p.a. compound interest for 2 years and R...
Given Data:
- Amount deposited at 10% p.a. for 2 years: Rs. X
- Amount deposited at 20% p.a. for 2 years: Rs. Y
- Overall interest is 35% of the overall amount
Solution:
Calculating Interest:
- Interest on amount X at 10% p.a. for 2 years = X * (1 + 0.10)^2 - X
- Interest on amount Y at 20% p.a. for 2 years = Y * (1 + 0.20)^2 - Y
Given:
- Overall interest = 35% of the overall amount
- Overall interest = Interest on X + Interest on Y
Equation:
35% * (X + Y) = X * (1 + 0.10)^2 - X + Y * (1 + 0.20)^2 - Y
Solving the Equation:
35% * (X + Y) = X * 1.21 - X + Y * 1.44 - Y
35% * (X + Y) = 0.21X + 0.44Y
35% * X + 35% * Y = 0.21X + 0.44Y
0.35X + 0.35Y = 0.21X + 0.44Y
0.14X = 0.09Y
X/Y = 9/14
Therefore, the ratio of X : Y is 9 : 14. Hence, option B is correct.
- Amount deposited at 10% p.a. for 2 years: Rs. X
- Amount deposited at 20% p.a. for 2 years: Rs. Y
- Overall interest is 35% of the overall amount
Solution:
Calculating Interest:
- Interest on amount X at 10% p.a. for 2 years = X * (1 + 0.10)^2 - X
- Interest on amount Y at 20% p.a. for 2 years = Y * (1 + 0.20)^2 - Y
Given:
- Overall interest = 35% of the overall amount
- Overall interest = Interest on X + Interest on Y
Equation:
35% * (X + Y) = X * (1 + 0.10)^2 - X + Y * (1 + 0.20)^2 - Y
Solving the Equation:
35% * (X + Y) = X * 1.21 - X + Y * 1.44 - Y
35% * (X + Y) = 0.21X + 0.44Y
35% * X + 35% * Y = 0.21X + 0.44Y
0.35X + 0.35Y = 0.21X + 0.44Y
0.14X = 0.09Y
X/Y = 9/14
Therefore, the ratio of X : Y is 9 : 14. Hence, option B is correct.
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Community Answer
Vishal deposited Rs. X at 10% p.a. compound interest for 2 years and R...
Interest of 2 years at 10% p.a.
Interest of 2 years at 20% p.a.
X : Y = 9 : 14
Hence, Option B is correct.
Interest of 2 years at 20% p.a.
X : Y = 9 : 14
Hence, Option B is correct.
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Vishal deposited Rs. X at 10% p.a. compound interest for 2 years and Rs. Y at 20% p.a. compound interest for 2 years. If his overall interest is 35% of the overall amount, what is X : Y?a)1 : 3b)9 : 14c)11 : 15d)12 : 17Correct answer is option 'B'. Can you explain this answer?
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