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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.
Most Upvoted Answer
Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in...
To find the second and last installments, let's first calculate the first installment.
Let the first installment be x.
According to the given condition, each installment is twice the preceding one. So, the second installment will be 2x, the third installment will be 4x, and so on.
Since there are 12 monthly installments, we can write the sum of the installments as follows:
x + 2x + 4x + 8x + ... + 2^10x = Rs. 32,760
Now, let's calculate the sum of this geometric series.
Sum = a(1 - r^n) / (1 - r)
where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = x, r = 2, and n = 11 (since we have 12 terms but we don't include the first term in the sum).
Sum = x(1 - 2^11) / (1 - 2)
= x(1 - 2048) / (-1)
= x(2047) / (-1)
= -2047x
Now, equating the sum to Rs. 32,760:
-2047x = 32,760
Dividing both sides by -2047:
x = -32,760 / 2047
x ≈ -16
Since installment amounts cannot be negative, we can take the absolute value of x:
x = 16
Therefore, the first installment is Rs. 16.
Next, let's find the second installment.
According to the given condition, the second installment is twice the first installment.
Second installment = 2 * 16 = Rs. 32
So, the second installment is Rs. 32.
Finally, let's find the last installment.
The last installment is the 12th installment, and it is twice the 11th installment.
11th installment = 2^10 * 16 = 2^10 * 2^4 = 2^14 = 16,384
Last installment = 2 * 16,384 = Rs. 32,768
So, the last installment is Rs. 32,768.
Therefore, the second installment is Rs. 32 and the last installment is Rs. 32,768.
Hence, the correct answer is option B) Rs. 16, Rs. 16,384.
Let the first installment be x.
According to the given condition, each installment is twice the preceding one. So, the second installment will be 2x, the third installment will be 4x, and so on.
Since there are 12 monthly installments, we can write the sum of the installments as follows:
x + 2x + 4x + 8x + ... + 2^10x = Rs. 32,760
Now, let's calculate the sum of this geometric series.
Sum = a(1 - r^n) / (1 - r)
where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = x, r = 2, and n = 11 (since we have 12 terms but we don't include the first term in the sum).
Sum = x(1 - 2^11) / (1 - 2)
= x(1 - 2048) / (-1)
= x(2047) / (-1)
= -2047x
Now, equating the sum to Rs. 32,760:
-2047x = 32,760
Dividing both sides by -2047:
x = -32,760 / 2047
x ≈ -16
Since installment amounts cannot be negative, we can take the absolute value of x:
x = 16
Therefore, the first installment is Rs. 16.
Next, let's find the second installment.
According to the given condition, the second installment is twice the first installment.
Second installment = 2 * 16 = Rs. 32
So, the second installment is Rs. 32.
Finally, let's find the last installment.
The last installment is the 12th installment, and it is twice the 11th installment.
11th installment = 2^10 * 16 = 2^10 * 2^4 = 2^14 = 16,384
Last installment = 2 * 16,384 = Rs. 32,768
So, the last installment is Rs. 32,768.
Therefore, the second installment is Rs. 32 and the last installment is Rs. 32,768.
Hence, the correct answer is option B) Rs. 16, Rs. 16,384.
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Mr. Seth borrows Rs. 32,760 without interest and agrees to pay back in...
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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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