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

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

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)

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: (d)

The percentage of students who pass in one or two or both subjects

= 60 + 70 – 40 = 90

Percentage of failed students = 100 – 90 = 10%

Answer: (d)

Number of students passed in first year = 75

Number of students passed in second year

= ${60 × 75}/100 = 45$

Total number of passed students = 75+45=120

Total number of appeared students =175

∴ Required percentage

= $120/175 × 100 = 68{4}/7%$

Answer: (c)

Failed candidates = ${1100 × 50}/100 + {900 × 60}/100$

= 550 + 540 = 1090

Required percentage = $1090/2000 × 100 = 54.5%$

Using Rule 25,

B = 1100, b = 50%, G = 900, g = 40%

Percentage of failed candidates = ${(Bb + Gg)}/{B + G}%$

= ${1100 × 50 + 900 × 40}/{1100 + 900}$

= ${55000 + 36000}/2000$

= $91/2$ = 45.5%