Answer

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**Hint:**First we will find subject wise percentage by using the formula

% = Marks scored $ \times $ 100 collectively divided by the Maximum marks and then the aggregate percentage by using the formula:

Aggregate % = Sum of marks scored in each subject $ \times $ 100 collectively divided by the sum of maximum marks of each subject.

**Complete step-by-step answer:**

Let us first calculate the percentage of Math:

Marks Scored in Math = 120 …….(1)

Maximum marks in Math = 150 …….(2)

Now, we will use the formula:

% = Marks scored $ \times $ 100 collectively divided by the Maximum marks ……….(3)

So, % in Math = $\dfrac{{120}}{{150}} \times 100 = \dfrac{4}{5} \times 100 = 80\% $

Let us now calculate the percentage of English:

Marks Scored in English = 136 …….(4)

Maximum marks in English = 200 …….(5)

Now, we will again use the formula mentioned in equation (3):

So, % in English = $\dfrac{{136}}{{200}} \times 100 = \dfrac{{136}}{2} = 68\% $

Let us now calculate the percentage of Science:

Marks Scored in Science = 108 …….(6)

Maximum marks in Science = 150 …….(7)

Now, we will again use the formula mentioned in equation (3):

So, % in Science = $\dfrac{{108}}{{150}} \times 100 = \dfrac{{108}}{3} \times 2 = 72\% $

Now, we need to find the aggregate percentage.

For aggregate percentage, we will use the following formula:

aggregate % = Sum of marks scored in each subject $ \times $ 100 collectively divided by the sum of maximum marks of each subject. ……(8)

For putting the values, let us first find the required values:

Sum of marks scored in each subject = Marks Scored in Math + Marks Scored in English + Marks Scored in Science

Using (1), (4) and (6), we get:

Sum of marks scored in each subject = 120 + 136 + 108 = 364 …….(9)

Sum of maximum marks of each subject = Maximum marks in Math + Maximum marks in English + Maximum marks in Science

Using (2), (5) and (7), we get:

Sum of maximum marks of each subject = 150 + 200 + 150 = 500 …….(10)

Putting (9) and (10) in (8), we get:

Aggregate % = $\dfrac{{364}}{{500}} \times 100 = \dfrac{{364}}{5} = 72.4\% $

Hence, we have found the required values.

**Note:**The students might make the mistake of multiplying by 100 in both the formulas. We must pay attention to the formulas.

The students also might get confused between average and percentage. Average is found by the sum of all the quantities divided by the number of quantities.

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