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### Question

The simple interest on a hypothetical investment is Rs. 5120. What is the principal amount if the rate per annum, time in years and the principal, all have the same numerical value?

**A**

Rs. 80.

**B**

Rs. 180.

**C**

Rs. 130.

**D**

Rs. 280.

**Soln.**

**Ans: a**

If I is the interest, and principal is P, time is P, and rate is P, then, I = $(P × P × P)/100$. Which gives P = $√^3{100 × I}$, which is $√^3{100 × 5120}$, which is $√^3{1000 × 8 × 8 × 8}$ = Rs. 80.