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A sum of Rs. 8800 is to be divided among three brothers Anil, Deepak and Ramesh in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 year respectively remains equal.
Quantity I: Share of Ramesh
Quantity II: Share of Anil
Quantity II: Share of Anil
- a)Quantity I > Quantity II
- b)Quantity I < Quantity II
- c)Quantity I ≥ Quantity II
- d)Quantity I ≤ Quantity II
- e)Quantity I = Quantity II or relation cannot be established
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A sum of Rs. 8800 is to be divided among three brothers Anil, Deepak a...
x*5*1/100 = y*5*2/100 = z*5*3/100
x:y:z = 6:3:2
Share of Ramesh = 2/11 * 8800 = 1600; Share of Anil = 6/11 * 8800 = 4800
x:y:z = 6:3:2
Share of Ramesh = 2/11 * 8800 = 1600; Share of Anil = 6/11 * 8800 = 4800
Most Upvoted Answer
A sum of Rs. 8800 is to be divided among three brothers Anil, Deepak a...
Understanding the Problem
We need to divide Rs. 8800 among three brothers—Anil, Deepak, and Ramesh—such that the simple interest on their respective shares at 5% per annum after 1, 2, and 3 years is equal.
Simple Interest Formula
The formula for simple interest (SI) is:
SI = (Principal × Rate × Time) / 100
Where:
- Principal = Share of the brother
- Rate = 5%
- Time = 1, 2, and 3 years for Anil, Deepak, and Ramesh respectively.
Let’s Define the Shares
- Let Anil's share = A
- Let Deepak's share = D
- Let Ramesh's share = R
From the problem, we can establish the following equations based on equal simple interest:
- For Anil (1 year): SI_A = (A × 5 × 1) / 100 = (A × 5) / 100
- For Deepak (2 years): SI_D = (D × 5 × 2) / 100 = (D × 10) / 100
- For Ramesh (3 years): SI_R = (R × 5 × 3) / 100 = (R × 15) / 100
Setting these equal gives:
(A × 5) / 100 = (D × 10) / 100 = (R × 15) / 100
Expressing Shares in Terms of Each Other
From the equations, we can express each share in terms of a common variable:
- A = 2D
- D = (1/2)A
- R = (1/3)A
Total Share Calculation
The total share can be represented as:
A + D + R = 8800
Substituting the values:
A + (1/2)A + (1/3)A = 8800
This can be simplified to find the individual shares. The calculations reveal:
Final Share Values
- A = 4800
- D = 2400
- R = 1600
Comparing Shares
Finally, we compare the shares:
- Share of Ramesh (R) = 1600
- Share of Anil (A) = 4800
Since 1600 < 4800,="" we="" />
Conclusion
The correct relation is:
Quantity I < quantity="" /> (Option B)
We need to divide Rs. 8800 among three brothers—Anil, Deepak, and Ramesh—such that the simple interest on their respective shares at 5% per annum after 1, 2, and 3 years is equal.
Simple Interest Formula
The formula for simple interest (SI) is:
SI = (Principal × Rate × Time) / 100
Where:
- Principal = Share of the brother
- Rate = 5%
- Time = 1, 2, and 3 years for Anil, Deepak, and Ramesh respectively.
Let’s Define the Shares
- Let Anil's share = A
- Let Deepak's share = D
- Let Ramesh's share = R
From the problem, we can establish the following equations based on equal simple interest:
- For Anil (1 year): SI_A = (A × 5 × 1) / 100 = (A × 5) / 100
- For Deepak (2 years): SI_D = (D × 5 × 2) / 100 = (D × 10) / 100
- For Ramesh (3 years): SI_R = (R × 5 × 3) / 100 = (R × 15) / 100
Setting these equal gives:
(A × 5) / 100 = (D × 10) / 100 = (R × 15) / 100
Expressing Shares in Terms of Each Other
From the equations, we can express each share in terms of a common variable:
- A = 2D
- D = (1/2)A
- R = (1/3)A
Total Share Calculation
The total share can be represented as:
A + D + R = 8800
Substituting the values:
A + (1/2)A + (1/3)A = 8800
This can be simplified to find the individual shares. The calculations reveal:
Final Share Values
- A = 4800
- D = 2400
- R = 1600
Comparing Shares
Finally, we compare the shares:
- Share of Ramesh (R) = 1600
- Share of Anil (A) = 4800
Since 1600 < 4800,="" we="" />
Conclusion
The correct relation is:
Quantity I < quantity="" /> (Option B)
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A sum of Rs. 8800 is to be divided among three brothers Anil, Deepak and Ramesh in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 year respectively remains equal.Quantity I: Share of RameshQuantity II: Share of Anila)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'B'. Can you explain this answer?
Question Description
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