A nine year old boys is 120 cm tall. If the present height of the boy is 75% of his full height, calculate the full height which the boy will eventually reach at the end of growth period.

Options

A. 160 cm
B. 170 cm
C. 180 cm
D. 190 cm

Answer

To solve the problem, we need to find the full height of the boy based on the information given. Here’s the step-by-step solution:

### Step 1: Understand the relationship between current height and full height
The problem states that the current height of the boy (120 cm) is 75% of his full height. This means that if we denote the full height as \( H \), we can express this relationship mathematically as:
\[ \text{Current Height} = 75\% \text{ of Full Height} \]
or
\[ 120 \text{ cm} = 0.75 \times H \]

### Step 2: Set up the equation
From the relationship established in Step 1, we can set up the equation:
\[ 120 = 0.75H \]

### Step 3: Solve for full height \( H \)
To find \( H \), we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.75:
\[ H = \frac{120}{0.75} \]

### Step 4: Calculate \( H \)
Now, we perform the calculation:
\[ H = \frac{120}{0.75} = 120 \times \frac{100}{75} = 120 \times \frac{4}{3} \]
Calculating this gives:
\[ H = 120 \times 1.3333 = 160 \text{ cm} \]

### Conclusion
The full height that the boy will eventually reach at the end of his growth period is **160 cm**.

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