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Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in 12 monthly installments, each being twice the preceding one. Find the 2nd and the last installment.
- a)Rs. 60, Rs. l5,600
- b)Rs.16, Rs. 16,384
- c)Rs.32, Rs.15,560
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in...
►The installments will form a GP with common ratio 2. The sum of this GP is 32760
= a(212 – 1) / (2 – 1).
►Solving this equation yields a = 8.
►Thus the 2nd installment is 8 x 2 = 16 and the last installment is 8 x 211 = 16384.
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Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in...
Dipak borrows Rs. 32,760 without interest and agrees to pay back in 12 monthly instalments, each instalment being twice the preceeding one. Find the second and the last instalments.
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Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in...
Given:
Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in 12 monthly installments, each being twice the preceding one.
To find:
The 2nd and the last installment.
Solution:
Let's assume the first installment to be x.
Calculating the installments:
The second installment will be twice the first installment = 2x.
The third installment will be twice the second installment = 2(2x) = 4x.
The fourth installment will be twice the third installment = 2(4x) = 8x.
And so on.
Calculating the sum of installments:
The sum of the installments can be calculated using the formula for the sum of a geometric series:
Sum = a(1 - r^n)/(1 - r)
Where:
a = first term
r = common ratio
n = number of terms
In this case, the first term (a) is x and the common ratio (r) is 2. Since there are 12 installments, n = 12.
Sum = x(1 - 2^12)/(1 - 2)
Sum = x(1 - 4096)/(-1)
Sum = x(4095)
Since the sum of the installments should be equal to the borrowed amount of Rs. 32,760:
x(4095) = 32760
x = 32760/4095
x = 8
Calculating the 2nd installment:
The second installment is twice the first installment, which is 2 * 8 = 16.
Calculating the last installment:
The last installment is the 12th installment, which is 8 * 2^(12-1) = 8 * 2^11 = 8 * 2048 = 16384.
Therefore, the 2nd installment is Rs. 16 and the last installment is Rs. 16,384.
Conclusion:
The 2nd installment is Rs. 16 and the last installment is Rs. 16,384. Thus, the correct answer is option B.
Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in 12 monthly installments, each being twice the preceding one.
To find:
The 2nd and the last installment.
Solution:
Let's assume the first installment to be x.
Calculating the installments:
The second installment will be twice the first installment = 2x.
The third installment will be twice the second installment = 2(2x) = 4x.
The fourth installment will be twice the third installment = 2(4x) = 8x.
And so on.
Calculating the sum of installments:
The sum of the installments can be calculated using the formula for the sum of a geometric series:
Sum = a(1 - r^n)/(1 - r)
Where:
a = first term
r = common ratio
n = number of terms
In this case, the first term (a) is x and the common ratio (r) is 2. Since there are 12 installments, n = 12.
Sum = x(1 - 2^12)/(1 - 2)
Sum = x(1 - 4096)/(-1)
Sum = x(4095)
Since the sum of the installments should be equal to the borrowed amount of Rs. 32,760:
x(4095) = 32760
x = 32760/4095
x = 8
Calculating the 2nd installment:
The second installment is twice the first installment, which is 2 * 8 = 16.
Calculating the last installment:
The last installment is the 12th installment, which is 8 * 2^(12-1) = 8 * 2^11 = 8 * 2048 = 16384.
Therefore, the 2nd installment is Rs. 16 and the last installment is Rs. 16,384.
Conclusion:
The 2nd installment is Rs. 16 and the last installment is Rs. 16,384. Thus, the correct answer is option B.
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Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in 12 monthlyinstallments, each being twice the preceding one. Find the 2ndand the last installment.a)Rs. 60, Rs. l5,600b)Rs.16, Rs. 16,384c)Rs.32, Rs.15,560d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in 12 monthlyinstallments, each being twice the preceding one. Find the 2ndand the last installment.a)Rs. 60, Rs. l5,600b)Rs.16, Rs. 16,384c)Rs.32, Rs.15,560d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in 12 monthlyinstallments, each being twice the preceding one. Find the 2ndand the last installment.a)Rs. 60, Rs. l5,600b)Rs.16, Rs. 16,384c)Rs.32, Rs.15,560d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in 12 monthlyinstallments, each being twice the preceding one. Find the 2ndand the last installment.a)Rs. 60, Rs. l5,600b)Rs.16, Rs. 16,384c)Rs.32, Rs.15,560d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in 12 monthlyinstallments, each being twice the preceding one. Find the 2ndand the last installment.a)Rs. 60, Rs. l5,600b)Rs.16, Rs. 16,384c)Rs.32, Rs.15,560d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in 12 monthlyinstallments, each being twice the preceding one. Find the 2ndand the last installment.a)Rs. 60, Rs. l5,600b)Rs.16, Rs. 16,384c)Rs.32, Rs.15,560d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in 12 monthlyinstallments, each being twice the preceding one. Find the 2ndand the last installment.a)Rs. 60, Rs. l5,600b)Rs.16, Rs. 16,384c)Rs.32, Rs.15,560d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
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