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### Question

An amount of Rs. 1000 is split into two parts. The first part is invested @5% for 4 years, and the second @11% for 16 years. What is the ratio of the first part is to the second part if they yield the same amount of simple interest?

**A**

$8{4/5}$.

**B**

$8{17/20}$.

**C**

$8{3/4}$.

**D**

$8{9/10}$.

**Soln.**

**Ans: a**

Let the amounts be x and y. We have x × r_{1} × t_{1} = y × r_{2} × t_{2}. We can see that x : y is same as r_{2}t_{2} : r_{1}t_{1}. The ratio is (11 × 16) : (5 × 4) = 176 : 20, or same as $8{4/5}$. *Please note that the answer is independent of the value of the total amount.*