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Mr. X invests 'P' amount at Simple Interest rate 10% and Mr. Y invests 'Q' amount at Compound Interest rate 5% compounded annually. At the end of two years both get the same amount of interest, then the relation between two amounts P and Q is given by: (a) P= 41Q/80 (b) P=41Q/40 (c) P=41Q/100 (d) P =41Q/200?
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Mr. X invests 'P' amount at Simple Interest rate 10% and Mr. Y invests...
**Solution:**
To solve this problem, we need to compare the interest earned by Mr. X and Mr. Y and then find the relation between the amounts P and Q.
Let's calculate the interest earned by Mr. X and Mr. Y.
**Interest earned by Mr. X:**
The formula to calculate simple interest is:
I = (P * R * T) / 100
Where,
I = Interest earned
P = Principal amount
R = Rate of interest
T = Time period
In this case, the principal amount is P, the rate of interest is 10%, and the time period is 2 years.
So, the interest earned by Mr. X is:
IX = (P * 10 * 2) / 100
IX = (20P) / 100
IX = 0.2P
**Interest earned by Mr. Y:**
The formula to calculate compound interest is:
A = P(1 + R/100)^T
Where,
A = Final amount
P = Principal amount
R = Rate of interest
T = Time period
In this case, the principal amount is Q, the rate of interest is 5% (compounded annually), and the time period is 2 years.
So, the final amount earned by Mr. Y is:
AY = Q(1 + 5/100)^2
AY = Q(1 + 0.05)^2
AY = Q(1.05)^2
AY = 1.1025Q
The interest earned by Mr. Y is the difference between the final amount and the principal amount:
IY = AY - Q
IY = 1.1025Q - Q
IY = 0.1025Q
Since it is given that both Mr. X and Mr. Y earn the same amount of interest, we can equate IX and IY:
0.2P = 0.1025Q
To find the relation between P and Q, we can simplify the equation:
P = (0.1025Q) / 0.2
P = 0.5125Q
Simplifying further, we get:
P = 41Q / 80
Therefore, the correct answer is option (a) P = 41Q / 80.
To solve this problem, we need to compare the interest earned by Mr. X and Mr. Y and then find the relation between the amounts P and Q.
Let's calculate the interest earned by Mr. X and Mr. Y.
**Interest earned by Mr. X:**
The formula to calculate simple interest is:
I = (P * R * T) / 100
Where,
I = Interest earned
P = Principal amount
R = Rate of interest
T = Time period
In this case, the principal amount is P, the rate of interest is 10%, and the time period is 2 years.
So, the interest earned by Mr. X is:
IX = (P * 10 * 2) / 100
IX = (20P) / 100
IX = 0.2P
**Interest earned by Mr. Y:**
The formula to calculate compound interest is:
A = P(1 + R/100)^T
Where,
A = Final amount
P = Principal amount
R = Rate of interest
T = Time period
In this case, the principal amount is Q, the rate of interest is 5% (compounded annually), and the time period is 2 years.
So, the final amount earned by Mr. Y is:
AY = Q(1 + 5/100)^2
AY = Q(1 + 0.05)^2
AY = Q(1.05)^2
AY = 1.1025Q
The interest earned by Mr. Y is the difference between the final amount and the principal amount:
IY = AY - Q
IY = 1.1025Q - Q
IY = 0.1025Q
Since it is given that both Mr. X and Mr. Y earn the same amount of interest, we can equate IX and IY:
0.2P = 0.1025Q
To find the relation between P and Q, we can simplify the equation:
P = (0.1025Q) / 0.2
P = 0.5125Q
Simplifying further, we get:
P = 41Q / 80
Therefore, the correct answer is option (a) P = 41Q / 80.
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Mr. X invests 'P' amount at Simple Interest rate 10% and Mr. Y invests 'Q' amount at Compound Interest rate 5% compounded annually. At the end of two years both get the same amount of interest, then the relation between two amounts P and Q is given by: (a) P= 41Q/80 (b) P=41Q/40 (c) P=41Q/100 (d) P =41Q/200?
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Mr. X invests 'P' amount at Simple Interest rate 10% and Mr. Y invests 'Q' amount at Compound Interest rate 5% compounded annually. At the end of two years both get the same amount of interest, then the relation between two amounts P and Q is given by: (a) P= 41Q/80 (b) P=41Q/40 (c) P=41Q/100 (d) P =41Q/200? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Mr. X invests 'P' amount at Simple Interest rate 10% and Mr. Y invests 'Q' amount at Compound Interest rate 5% compounded annually. At the end of two years both get the same amount of interest, then the relation between two amounts P and Q is given by: (a) P= 41Q/80 (b) P=41Q/40 (c) P=41Q/100 (d) P =41Q/200? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. X invests 'P' amount at Simple Interest rate 10% and Mr. Y invests 'Q' amount at Compound Interest rate 5% compounded annually. At the end of two years both get the same amount of interest, then the relation between two amounts P and Q is given by: (a) P= 41Q/80 (b) P=41Q/40 (c) P=41Q/100 (d) P =41Q/200?.
Mr. X invests 'P' amount at Simple Interest rate 10% and Mr. Y invests 'Q' amount at Compound Interest rate 5% compounded annually. At the end of two years both get the same amount of interest, then the relation between two amounts P and Q is given by: (a) P= 41Q/80 (b) P=41Q/40 (c) P=41Q/100 (d) P =41Q/200? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Mr. X invests 'P' amount at Simple Interest rate 10% and Mr. Y invests 'Q' amount at Compound Interest rate 5% compounded annually. At the end of two years both get the same amount of interest, then the relation between two amounts P and Q is given by: (a) P= 41Q/80 (b) P=41Q/40 (c) P=41Q/100 (d) P =41Q/200? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. X invests 'P' amount at Simple Interest rate 10% and Mr. Y invests 'Q' amount at Compound Interest rate 5% compounded annually. At the end of two years both get the same amount of interest, then the relation between two amounts P and Q is given by: (a) P= 41Q/80 (b) P=41Q/40 (c) P=41Q/100 (d) P =41Q/200?.
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