A few buy National Savings Certificates each year whose worth surpasses the…
2023
A few buy National Savings Certificates each year whose worth surpasses the earlier years buy by Rs 400. Following 8 years, she finds that she has obtained declarations whose aggregate faceworth is Rs 48000. What is the face estimation of the Certificates acquired by her in the first years?
- A.
Rs. 43000
- B.
Rs. 44000
- C.
Rs. 45000
- D.
Rs. 46000
Attempted by 16 students.
Show answer & explanation
Correct answer: D
Key idea: the certificates bought each year form an arithmetic progression; use the sum formula to find the first term.
Let the face value of the certificates bought in the first year be a. Common difference d = 400, number of years n = 8, and total S_n = 48000.
Use the sum formula for an arithmetic series: S_n = n/2 [2a + (n - 1)d].
Substitute the known values: 48000 = 8/2 [2a + (8 - 1)·400] = 4 [2a + 7·400].
Calculate inside the brackets: 7·400 = 2800, so 48000 = 4(2a + 2800) ⇒ 2a + 2800 = 48000/4 = 12000.
Solve for a: 2a = 12000 − 2800 = 9200 ⇒ a = 9200/2 = 4600.
Conclusion: The face value of the certificates bought in the first year is Rs. 4600.
Note on the provided options: None of the given options exactly match Rs. 4600. The option shown as "Rs. 46000" appears to contain an extra zero and is likely a typographical error. If that option were intended to be "Rs. 4600" it would be the correct choice; as printed, Rs. 46000 does not equal the computed value.