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A man arranges to pay off an interest-free debt of Rs. 7,200 in 20 instalments which form an A.R When the first 15 instalments are paid, he finds that one-third of his debt still remains unpaid.What amount (in Rs.) does he pay as his 16th instalment?
- a)448
- b)368
- c)288
- d)384
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A man arranges to pay off an interest-free debt of Rs. 7,200 in 20 ins...
Let the first term and common difference of the A.P. be a and d respectively.
Sum of 20 terms of this A.P. = 7200 (20/2) x [2a + (20 - 1 )d] = 7200 2a+19d=720... (i)
Sum of first 15 terms of this A.P. = (2/3) x 7200 = 4800
(15/2) x [2a + (15 - 1)d] = 4800
2a + 14o/ = 640 ... (ii)
Solving (i) and (ii) gives d = 16 and a = 208 16th instalment = a + 15d = 208 + 15(16) = Rs. 448
Hence, option 1.
Most Upvoted Answer
A man arranges to pay off an interest-free debt of Rs. 7,200 in 20 ins...
Given:
- Interest-free debt = Rs. 7,200
- Number of instalments = 20
- First 15 instalments paid
- One-third of debt still remains unpaid
To find: Amount paid as 16th instalment
Approach:
Let's assume that each instalment is of Rs. x
- Total amount to be paid = 20x
- Amount paid in first 15 instalments = 15x
- Remaining amount = 7200 - 15x
- One-third of debt still remains unpaid, i.e. (7200 - 15x)/3 = 2400 - 5x
- Remaining instalments = 20 - 15 = 5
Now, we can form an A.R. with the remaining instalments:
a, a + d, a + 2d, a + 3d, a + 4d
where a = amount of 16th instalment = ?
d = common difference between the instalments
We know that one-third of the debt is still remaining after 15 instalments, i.e. 2400 - 5x.
So, the sum of remaining 5 instalments should be equal to this amount.
Sum of remaining 5 instalments = (5/2) [2a + 4d] = 5a + 10d
Therefore, we can form an equation:
5a + 10d = 2400 - 5x
We also know that the total amount paid should be equal to the original debt of Rs. 7,200:
15x + 5a + 10d = 7200
We have two equations:
5a + 10d = 2400 - 5x
15x + 5a + 10d = 7200
Solving these equations, we get:
a = 448
Therefore, the man pays Rs. 448 as his 16th instalment.
- Interest-free debt = Rs. 7,200
- Number of instalments = 20
- First 15 instalments paid
- One-third of debt still remains unpaid
To find: Amount paid as 16th instalment
Approach:
Let's assume that each instalment is of Rs. x
- Total amount to be paid = 20x
- Amount paid in first 15 instalments = 15x
- Remaining amount = 7200 - 15x
- One-third of debt still remains unpaid, i.e. (7200 - 15x)/3 = 2400 - 5x
- Remaining instalments = 20 - 15 = 5
Now, we can form an A.R. with the remaining instalments:
a, a + d, a + 2d, a + 3d, a + 4d
where a = amount of 16th instalment = ?
d = common difference between the instalments
We know that one-third of the debt is still remaining after 15 instalments, i.e. 2400 - 5x.
So, the sum of remaining 5 instalments should be equal to this amount.
Sum of remaining 5 instalments = (5/2) [2a + 4d] = 5a + 10d
Therefore, we can form an equation:
5a + 10d = 2400 - 5x
We also know that the total amount paid should be equal to the original debt of Rs. 7,200:
15x + 5a + 10d = 7200
We have two equations:
5a + 10d = 2400 - 5x
15x + 5a + 10d = 7200
Solving these equations, we get:
a = 448
Therefore, the man pays Rs. 448 as his 16th instalment.
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A man arranges to pay off an interest-free debt of Rs. 7,200 in 20 instalments which form an A.R When the first 15 instalments are paid, he finds that one-third of his debt still remains unpaid.What amount (in Rs.) does he pay as his 16th instalment?a)448b)368c)288d)384Correct answer is option 'A'. Can you explain this answer?
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