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**Hint:**Assume the original weight of Amir, i.e., weight before going to gym as x. Find his weight after he lost 10% of the original weight by subtracting 10% of x from x. Now, to find the percentage that Amir must gain, consider the above calculates weight as initial weight, x as the final weight and use the formula: - Percentage gain = (final weight – initial weight / initial weight) \[\times 100%\].

**Complete step by step solution:**

Here, we have been given that Amir loses 10% of his original weight in the gym. We have been asked to determine the weight percentage that Amir must gain so that he could return to his original weight.

Now, let us assume that the original weight of Amir was ‘x’ kg. It is said that he lost 10% of this weight in the gym, so we have,

\[\Rightarrow \] Weight loss by Amir = 10% of x

\[\Rightarrow \] Weight loss by Amir = \[\dfrac{10}{100}\times x\]

\[\Rightarrow \] Weight loss by Amir = \[\dfrac{x}{10}\]

Therefore, Amir's current weight will be the difference of his original weight and the weight lost. So, we have,

\[\Rightarrow \] Current weight of Amir = \[x-\dfrac{x}{10}\]

\[\Rightarrow \] Current weight of Amir = \[\dfrac{9x}{10}\]

\[\Rightarrow \] Current weight of Amir = (0.9x) kg

Now, it is said that Amir has to return to his original weight, i.e., x kg, that means he has to gain weight. So, we have,

\[\Rightarrow \] Weight to be gained by Amir so that he can return to his original weight = x – 0.9x = 0.1x.

We know that gain percentage = (Gain / Initial value) \[\times 100%\], so here in the above case, we have,

\[\Rightarrow \] Gain = 0.1x, Initial value = 0.9x

So, substituting these values in the above formula, we get,

\[\Rightarrow \] Weight percentage that must be gained by Amir = \[\left( \dfrac{0.1x}{0.9x} \right)\times 100%\]

Removing the decimal and simplifying we get,

\[\Rightarrow \] Weight percentage that must be gained by Amir = 11.11%.

**Hence, the weight percent gain required is 11.11%, which is our answer.**

**Note:**One may make a mistake by thinking that if he lost 10%. Weight then to come to the previous weight he must gain 10% weight, but that is not the case. The reason is that the value of weight will be changed when he loses it. So, when will apply the percentage gain formula, the initial weight will be his current weight, i.e., \[\dfrac{9x}{10}\]. Do not consider the initial weight as x otherwise you will get the wrong answer.

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