model 7 marks scored in examinations Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

25% of students pass in at least one subject i.e.; they pass in one or both subjects.

% of students who don't pass or fail in both subjects

= (100 – 25)% = 75%

Answer: (a)

Let total number of candidates = 100

70 candidates passed in English and 30 failed in it.

80 candidates passed in Maths and 20 failed in it.

10 candidates failed in English and Maths both.

Out of 30 failed in English, 10 failed in Maths also.

30 – 10 = 20 failed in English alone.

Similarly, 20 – 10 = 10 failed in Maths alone.

Total number of failures = 20 + 10 + 10 = 40

100 – 40 = 60 candidates passed in both subjects.

Now, if 60 candidates pass, total strength = 100

For 144 candidates, total strength = $100/60 × 144$ = 240

Answer: (a)

Let the maximum marks be x.

According to question,

20% of x + 5 = 30% of x –20

(30 –20)% of x = 25

x = ${25 × 100}/10 = 250$

Passing marks = 20% of 250 + 5 = 55

% Passing marks = $55/250 × 100 = 22%$

Using Rule 22,

Here, m = 30%, n = 20%, p = 5 and q = 20

Maximum marks = $100/\text"(n - m)" × (p + q)$

= $100/{(30 - 20)} × (5 + 20)$

= ${100 × 25}/10 = 250$

Passing marks = 20% of 250 + 5 = 55

% of passing marks = $55/250 × 100$ = 22%

Answer: (d)

n(M) = 65, n(P) = 48, n(M?P) = 30

n(M?P)= n(M) + n(P) – n(M?P)

= 65 + 48 – 30 = 83

Percent of students passed = 83

Percent of students failed= 17

Method 2 :

Students passed only in Math = 65 – 30 = 35%

Students passed only in Physics = 48 – 30 = 18%

Total passing % = 35 + 18 + 30 = 83%

Failed = 100 – 83 = 17%

Answer: (c)

Total number of students = 640 + 360 = 1000

Number of successful boys = 60% of 640 = 384

Number of successful girls = 80% of 360 = 288

Total number of successful students = 384 + 288 = 672

Number of unsuccessful students = 1000 – 672 = 328

Required percentage = ${328 × 100}/1000 = 32.8%$

Using Rule 25,

B = 640, G = 360, b = 60%, g = 80%

Percentage of passed students = $({Bb + Gg}/{B + G})%$

= ${640 × 60 + 360 × 80}/{640 + 360}$

= ${38400 + 28800}/1000 = 67200/1000 = 67.2%$

% of failed students = 100 – 67.2% = 32.8%

Answer: (d)

Let the full marks in that examination were x.

According to the question,

${30x}/100 + 5 = {40x}/100 - 10$

${4x}/10 - {3x}/10 = 10 + 5$

$x/10 = 15$ ∴ x = 150

Minimum pass marks

$30/100 × 150 + 5 = 50$

Using Rule 22,

m = 30%, n = 40%, p = 5, q = 10.

Maximum marks = $100/{(n - m)} × (p + q)$

= $100/{(40 - 30)} × (5 + 10) = 150$

Minimum passing marks = $150 × 30/100 + 5$

= 45 + 5 = 50