A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?

Question: A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?

Solution:
According to the question,
Principal + Simple interest for 2 years = Tk. 720 ------------- (1)
Principal + Simple interest for 7 years = Tk. 1020 ------------ (2)

Subtracting equation (1) from (2)
Principal + Simple interest for 7 years = Tk. 1020
Principal + Simple interest for 2 years = Tk. 720
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∴ Simple interest for 5 years = Tk. 300
⇒ Simple interest for 1 years = Tk. 300/5
⇒ Simple interest for 1 year = Tk. 60
⇒ Simple interest for 2 years = Tk. (60 × 2)
∴ Simple interest for 2 years = = Tk. 120

∴ Principal amount = (Amount after 2 years - 2 years Simple interest)
⇒ Principal amount = Tk. (720 - 120)
∴ Principal amount = Tk. 600