Question

In an exam a student gets 30% marks and fails by 20 marks. But if he would have scored 25 marks more.Than passing he would have got 41.25%. find his full marks of paper and passing marks as well.

Answer 1

Step-by-step explanation:

Question-

In an exam a student gets 30% marks and fails by 20 marks. But if he would have scored 25 marks more.Than passing he would have got 41.25%. Find his full marks of paper and passing marks.

Given-

1st condition-

A student gets 30% marks and fails by 20 marks.

2nd condition-

If he would have scored 25 marks more then he would have got 41.25%.

To Find-

Full marks of paper and passing marks.

Solution-

✇ Let us consider that the full marks of paper be x.

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$\bigstar \rm \: 1st \: condition$

$\sf \: Passing \: marks = \\ \\ \sf➻ \: 30\% \: of \: (x + 12) \\ \\➻ \bf \: \frac{30}{100} (x + 12)$

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$\bigstar \rm \: 2nd \: condition$

$\: \sf \: Passing \: marks = \\ \\ \sf \: ➟ \: 41.25\% \: of \: (x - 25) \\ \\ ➟ \sf \frac{41.25}{100} (x - 25) \\ \\ ➟ \bf \: \frac{4125}{10000}(x - 25)$

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Now,

ACQ,

$\therefore \sf \: \frac{30}{100} (x + 12) = \frac{4125}{10000} (x - 25) \\ \\ ➳\sf \: 3000(x + 12) = 4125(x - 25) \\ \\ ➳ \sf \: 3000x + 36000 = 4125x - 103125 \\ \\ ➳ \sf \: 3000 - 4125x = - 103125 - 36000 \\ \\ ➳ \sf \: \cancel - 125x = \cancel - 139125 \\ \\ ➳ \bf \huge \boxed{ \red{ \bf \: x = 1113}}$

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$\boxed{\sf \clubs \Large \: \purple{\bf Total\: marks = 1113}}$

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Now to find the passing marks we can put the value of x in any condition.

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$\boxed{array}{c}\sf \: Passing \: marks = \frac{30}{100} \times (x+12) \\ \\ \dashrightarrow \sf\frac{30}{100}×(1113+12)\\ \\ \sf\dashrightarrow \frac{3\cancel{0}}{1\cancel{00}}×1130 \\ \\ \sf 3×113\\ \\ \pink{\boxed{\Large \bf 339 \:marks }}$

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$\underline{ \sf\tiny \green{\therefore Total{(marks)} \: and\:Passing{(marks)} \:are\: 1139 \:and \: 339\: respectively}}$

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Answer 2

Let :-

• The total mark be x

Given :-

• Mark secured by students = 30%
• The student fail by = 20 mark
• Passing mark in exam = 41.25%

To Find :-

• (i) Marks secured by the student = ?
• (ii) Passing mark in his exam = ?

Solution :-

• To calculate the marks secured by student and passing marks in his exam , at first we have to calculate the total marks in his exam then calculate passing mark and his mark that he secured.

Calculation begins :-

• Passing marks of total marks 30% of total marks of the students plus add 20 marks and 25 marks. Here 20 marks is the mark so that students fail and 25 mark is extra marks for the students for passing mark.

⇒41.25% × X = 30% × X + 20 + 25

⇒41.25X/100 = 30X/100 + 45

⇒41.25X/100 - 30X/100 = 45

⇒41.25X - 30X/100 = 45

⇒11.25X/100 = 45

⇒11.25X = 4500

⇒X = 400

Let's calculate his marks and passing mark in his exam :-

• Passing in his exam :-

⇒ Total marks of 41.25%

⇒ 400 × 41.25/100

⇒ 4 × 41.25

⇒ 165 marks

• Marks secured by the students :-

⇒ Total marks of 30% + 20

⇒ 400 × 30/100 + 20

⇒ 4 × 30 + 20

⇒ 120 + 20

⇒ 140 marks

Hence,

• Marks secured by student = 140
• Passing mark in his exam = 165