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P and Q invest some amount under SI and CI respectively but for the same period at 6% per annum. Each gets a total amount of Rs. 65,000 at the end of 6 years. Which of the following is definitely true?(i) Q’s initial principal is less than that of P(ii) Q’s initial principal is equal to that of P(iii) P’s percentage earning is less than that of Q
- a)(i) only
- b)(ii) only
- c)(iii) only
- d)(i) and (iii) only
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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P and Q invest some amount under SI and CI respectively but for the sa...
Earns more interest than P
(ii) Q earns less interest than P
(iii) Q earns the same interest as P
To find the answer, we can set up two equations using the formulas for simple interest and compound interest.
For P:
Principal (P) = x (amount invested)
Rate (R) = 6% or 0.06
Time (T) = 6 years
Simple Interest (SI) = P * R * T
CI = P * (1 + R)^T
For Q:
Principal (Q) = y (amount invested)
Rate (R) = 6% or 0.06
Time (T) = 6 years
Simple Interest (SI) = Q * R * T
CI = Q * (1 + R)^T
We are given that the total amount for both P and Q is Rs. 65,000, so we can set up the following equation:
P + Q = 65,000
Now, we need to compare the interest earned by P and Q. To do this, we can compare the total amount earned (principal + interest) by P and Q.
For P:
Total amount earned by P = P + SI = P + P * R * T = P(1 + R * T)
For Q:
Total amount earned by Q = Q + CI = Q + Q * (1 + R)^T
Since both P and Q earn the same total amount of Rs. 65,000, we can set up the following equation:
P(1 + R * T) = Q + Q * (1 + R)^T
Simplifying the equation, we get:
P + P * R * T = Q + Q * (1 + R)^T
P * R * T = Q * (1 + R)^T - Q
P * R * T = Q * [(1 + R)^T - 1]
Since P = 65,000 - Q, we can substitute this into the equation:
(65,000 - Q) * R * T = Q * [(1 + R)^T - 1]
Simplifying further, we get:
65,000 * R * T - Q * R * T = Q * [(1 + R)^T - 1]
65,000 * R * T = Q * [(1 + R)^T - 1] + Q * R * T
65,000 * R * T = Q * [(1 + R)^T - 1 + R * T]
Dividing both sides by Q, we get:
65,000 * R * T / Q = (1 + R)^T - 1 + R * T
Since R = 0.06 and T = 6, we can substitute these values:
65,000 * 0.06 * 6 / Q = (1 + 0.06)^6 - 1 + 0.06 * 6
Simplifying further, we get:
23.4 = (1.06)^6 - 1 + 0.36
23.4 = 1.41851 - 1 + 0.36
23.4 = 0.77851 + 0.36
23.4 = 1.13851
This is not true, so our initial assumption that Q earns more interest
(ii) Q earns less interest than P
(iii) Q earns the same interest as P
To find the answer, we can set up two equations using the formulas for simple interest and compound interest.
For P:
Principal (P) = x (amount invested)
Rate (R) = 6% or 0.06
Time (T) = 6 years
Simple Interest (SI) = P * R * T
CI = P * (1 + R)^T
For Q:
Principal (Q) = y (amount invested)
Rate (R) = 6% or 0.06
Time (T) = 6 years
Simple Interest (SI) = Q * R * T
CI = Q * (1 + R)^T
We are given that the total amount for both P and Q is Rs. 65,000, so we can set up the following equation:
P + Q = 65,000
Now, we need to compare the interest earned by P and Q. To do this, we can compare the total amount earned (principal + interest) by P and Q.
For P:
Total amount earned by P = P + SI = P + P * R * T = P(1 + R * T)
For Q:
Total amount earned by Q = Q + CI = Q + Q * (1 + R)^T
Since both P and Q earn the same total amount of Rs. 65,000, we can set up the following equation:
P(1 + R * T) = Q + Q * (1 + R)^T
Simplifying the equation, we get:
P + P * R * T = Q + Q * (1 + R)^T
P * R * T = Q * (1 + R)^T - Q
P * R * T = Q * [(1 + R)^T - 1]
Since P = 65,000 - Q, we can substitute this into the equation:
(65,000 - Q) * R * T = Q * [(1 + R)^T - 1]
Simplifying further, we get:
65,000 * R * T - Q * R * T = Q * [(1 + R)^T - 1]
65,000 * R * T = Q * [(1 + R)^T - 1] + Q * R * T
65,000 * R * T = Q * [(1 + R)^T - 1 + R * T]
Dividing both sides by Q, we get:
65,000 * R * T / Q = (1 + R)^T - 1 + R * T
Since R = 0.06 and T = 6, we can substitute these values:
65,000 * 0.06 * 6 / Q = (1 + 0.06)^6 - 1 + 0.06 * 6
Simplifying further, we get:
23.4 = (1.06)^6 - 1 + 0.36
23.4 = 1.41851 - 1 + 0.36
23.4 = 0.77851 + 0.36
23.4 = 1.13851
This is not true, so our initial assumption that Q earns more interest
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P and Q invest some amount under SI and CI respectively but for the same period at 6% per annum. Each gets a total amount of Rs. 65,000 at the end of 6 years. Which of the following is definitely true?(i) Q’s initial principal is less than that of P(ii) Q’s initial principal is equal to that of P(iii) P’s percentage earning is less than that of Qa)(i) onlyb)(ii) onlyc) (iii) onlyd)(i) and (iii) onlye)None of theseCorrect answer is option 'D'. Can you explain this answer?
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P and Q invest some amount under SI and CI respectively but for the same period at 6% per annum. Each gets a total amount of Rs. 65,000 at the end of 6 years. Which of the following is definitely true?(i) Q’s initial principal is less than that of P(ii) Q’s initial principal is equal to that of P(iii) P’s percentage earning is less than that of Qa)(i) onlyb)(ii) onlyc) (iii) onlyd)(i) and (iii) onlye)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about P and Q invest some amount under SI and CI respectively but for the same period at 6% per annum. Each gets a total amount of Rs. 65,000 at the end of 6 years. Which of the following is definitely true?(i) Q’s initial principal is less than that of P(ii) Q’s initial principal is equal to that of P(iii) P’s percentage earning is less than that of Qa)(i) onlyb)(ii) onlyc) (iii) onlyd)(i) and (iii) onlye)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P and Q invest some amount under SI and CI respectively but for the same period at 6% per annum. Each gets a total amount of Rs. 65,000 at the end of 6 years. Which of the following is definitely true?(i) Q’s initial principal is less than that of P(ii) Q’s initial principal is equal to that of P(iii) P’s percentage earning is less than that of Qa)(i) onlyb)(ii) onlyc) (iii) onlyd)(i) and (iii) onlye)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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