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**Hint:**In both the questions, we will, first of all, assume the variable for the present age. Now, the age after some years would be calculated by adding the percentage to that years, and finally, by applying the given condition in the question we will calculate the present age.

**Complete step-by-step solution**(i) Let us first solve part (i). We are given that after 16 years, Fatima will be 3 times as old as she is now.

Let the present age of Fatima be x. Then after 16 years, his age will be x + 16.

Now, as we are given that Fatima will be 3 times x, then

\[\Rightarrow 3x=x+16\]

\[\Rightarrow 3x-x=16\]

\[\Rightarrow 2x=16\]

Dividing both the sides by 2, we get,

\[\Rightarrow x=8\]

Therefore, the present age of Fatima is 8 years.

Hence, part (i) answer is 8 years.

(ii) Now, let us consider part (ii).

Let Rahim’s present age be y. We are given that after 32 years, Rahim would be 5 times as old as he was 8 years ago. After 32 years, Rahim’s age will be y + 32 and the age of Rahim 8 years ago would be (y – 8). Then according to the given condition of the question, we have,

\[y+32=5\left( y-8 \right)\]

\[\Rightarrow y+32=5y-40\]

\[\Rightarrow 5y-y=40+32\]

\[\Rightarrow 4y=\dfrac{72}{4}\]

\[\Rightarrow y=18\]

**Therefore, the present age of Rahim is 18 years. Hence, the answer to (ii) is 18 years.**

**Note:**A key point to note here in this question is that while solving such questions, always remember that if the present age of a person is t years, then after x years, his age would be $t + x$ and before y years, his age would be $t – y.$

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