Simple Interest – Find the principal from two amounts: A sum amounts to Rs 2,240 in 2 years and Rs 2,600 in 5 years at simple interest. Find the principal (original sum).

Difficulty: Easy

Correct Answer: Rs 2000

Explanation:


Introduction / Context:
Two amounts at different times let us compute the uniform annual SI and hence the principal in a linear SI model.



Given Data / Assumptions:

  • A2 = Rs 2240
  • A5 = Rs 2600


Concept / Approach:
Annual SI = (A5 - A2) / (5 - 2). Then P = A2 - 2 * (annual SI).



Step-by-Step Solution:

Annual SI = (2600 - 2240) / 3 = 360 / 3 = Rs 120P = 2240 - 2 * 120 = 2240 - 240 = Rs 2000


Verification / Alternative check:

A5 check: 2000 + 5 * 120 = 2600 (matches)


Why Other Options Are Wrong:

  • Rs 1880 / 2120 / 1960: do not fit both given amounts.
  • Data inadequate: sufficient for SI.


Common Pitfalls:

  • Mistaking the time gap.


Final Answer:
Rs 2000.

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