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?

  1. A.

    Rs. 43000

  2. B.

    Rs. 44000

  3. C.

    Rs. 45000

  4. 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.

  1. 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.

  2. Use the sum formula for an arithmetic series: S_n = n/2 [2a + (n - 1)d].

  3. Substitute the known values: 48000 = 8/2 [2a + (8 - 1)·400] = 4 [2a + 7·400].

  4. Calculate inside the brackets: 7·400 = 2800, so 48000 = 4(2a + 2800) ⇒ 2a + 2800 = 48000/4 = 12000.

  5. Solve for a: 2a = 12000 − 2800 = 9200 ⇒ a = 9200/2 = 4600.

  6. Conclusion: The face value of the certificates bought in the first year is Rs. 4600.

  7. 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.

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