model 7 marks scored in examinations Practice Questions Answers Test with Solutions & More Shortcuts

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: (b)

Clearly, 75 candidates qualify

75% of appearing candidates = 450

Number of appearing candidates

= ${450 × 100}/75 = 600$

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%