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Question

Girish scored 572 marks in an examination and was 30 marks short of 28% of maximum marks. In the same examination, his friend scored 473 marks. What is the percentage of marks scored by his friend?

The correct answer is
22%

Marks: Find Maximum Examination Marks

Let the maximum marks for the examination be denoted by M.

Girish scored 572 marks.

This score was 30 marks less than 28% of the maximum marks.

This means that 28% of the maximum marks is equal to Girish's score plus the deficit:

$ 0.28 \times M = 572 + 30 $

$ 0.28 \times M = 602 $

To find the maximum marks M, we rearrange the equation:

$ M = \frac{602}{0.28} $

$ M = \frac{60200}{28} $

$ M = 2150 $

So, the maximum marks for the examination were 2150.

Percentage: Calculate Friend's Score Percentage

Girish's friend scored 473 marks.

The maximum marks are 2150.

To find the percentage of marks scored by the friend, we use the formula:

$ \text{Percentage} = \left( \frac{\text{Score Obtained}}{\text{Maximum Marks}} \right) \times 100 $

Substituting the values:

$ \text{Friend's Percentage} = \left( \frac{473}{2150} \right) \times 100 $

$ \text{Friend's Percentage} = \frac{47300}{2150} $

$ \text{Friend's Percentage} = \frac{4730}{215} $

$ \text{Friend's Percentage} = 22\% $

Therefore, the friend scored 22% of the maximum marks.

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Important Questions from Percentage (Notes)

  1. 20% of a number is more than 20% of 620 by 210. The number is:
  2. Anubhav spent 14% of his income on electricity bills, 28% on rent and 18% on shopping. If $\frac{1}{4}$ th of the remaining amount is ₹5120, how much did he spend on electricity bills ?
  3. The total population of a town is 50,000. The number of males and females increases by 10% and 15% respectively and consequently the population of the town becomes 56,000. What was the number of males in the town?
  4. There is an increase of 30% in the number of people coming to a theatre after reducing the entry fee by 25% per person. How much change is expected in the total earnings?
  5. Gokul donates $17\%$ of his savings to old age home, $17\%$ of the savings to orphanage and $17\%$ of his savings to foundations for medical help. The remaining amount of Rs.$9800$ of savings is been deposited in bank. Find the salary of Gokul, if $50\%$ of the salary is his savings amount. (In Rs.)
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