An instrument cost a certain factory Rs. 520,000. If it depreciates in value…

2020

An instrument cost a certain factory Rs. 520,000. If it depreciates in value by 16.5% the first year, 15% the next year, 13.5% the third year, and so on, what will be its value (in Rs.) at the end of 8 years, all percentages applying to the original cost?

Answer: D. 52000 — CONCEPT: When each depreciation rate is applied to the original cost, the losses add directly as percentages of that original cost. For rates that form an…

  1. A.

    57500

  2. B.

    65000

  3. C.

    62000

  4. D.

    52000

Attempted by 6 students.

Show answer & explanation

Correct answer: D

CONCEPT: When each depreciation rate is applied to the original cost, the losses add directly as percentages of that original cost.

For rates that form an arithmetic sequence, use the arithmetic-series sum to get the total depreciation percentage, then subtract that percentage from 100% to find the remaining value.

APPLICATION:

  1. The 8 yearly rates are 16.5%, 15%, 13.5%, 12%, 10.5%, 9%, 7.5%, and 6%.

  2. Their sum is n/2[2a + (n - 1)d] = 8/2[2(16.5) + 7(-1.5)] = 4(33 - 10.5) = 90%.

  3. So the total depreciation is 90% of Rs. 520,000 = Rs. 468,000.

  4. The value left is Rs. 520,000 - Rs. 468,000 = Rs. 52,000.

CROSS-CHECK: If 90% of the original cost is depreciated, 10% remains; 10% of Rs. 520,000 is Rs. 52,000.

Result: the value at the end of 8 years is Rs. 52,000.

Explore the full course: Iocl Engineers Officer Grade A Paper 1

Loading lesson…