Directions: The following table shows the percentage of marks obtained by six students in five different subjects. Answer the following questions based on this table.

Students
 Physics (Out of 75)
 Chemistry (Out of 75)
 Maths (Out of 200)
 Hindi (Out of 50)
 English (Out of 150)
A 84% 42% 67% 44% 74%
B 68% 64% 49% 74% 52%
C 72% 54% 58% 68% 64%
D 48% 82% 63% 48% 70%
E 70% 78% 71% 56% 78%
F 56% 66% 55% 76% 66%
Important for :
1
What is the average marks scored by all the students in Physics?
» Explain it
A
Average marks of all students in Physics

 = 1 × 75 [84% + 68% + 72% + 48% + 70% + 56%] 6

 ⇒ 1 × 75% [84 + 68 + 72 + 48 + 70 + 56] 6

 ⇒ 1 × 75 [398] = 49.75 6 100

Hence, option A is correct.

2
What is the total marks scored by Student F in all the subjects together?
» Explain it
E
Total marks scored by student F in all the subject together =

= (75 × 56%) + ( 75 × 66%) + ( 200 × 55%) + (50 × 76%) + (150 × 66%)

 = (75 × 56) + (75 × 66) + (200 × 55) + (50 × 76) + (150 × 66) 100 100 100 100 100

= 42 + 49.5 + 110 + 38 + 99 = 338.5

Hence, option E is correct.
3
What is the overall percentage of marks scored by Student B? (Answer approximate value.)
» Explain it
B
= (75 × 68%) + ( 75 × 64%) + ( 200 × 49%) + (50 × 74%) + (150 × 52%)

 ⇒ (75 × 68) + (75 × 64) + (200 × 49) + (50 × 74) + (150 × 52) 100 100 100 100 100
⇒   51 + 48 + 98 + 37 + 78 = 312

 Reqd% = 312 × 100 = 56.72 ≈ 57% 550

Hence, option B is correct.
4
The marks scored by Student C in physics is approximately what per cent of the marks scored by him in English?
» Explain it
A
Total marks scored by Student C in physics

 = 72 × 75 = 54 100

Total marks scored by Student C in English

 = 64 × 150 = 96 100

 Reqd% = 54 × 100 = 56.25 ≈ 56% 96

Hence, option A is correct.
5
What is the difference between the total marks obtained by Student D in Chemistry and English and that obtained by Student F in the same subject?
» Explain it
C
Total marks of Student D in Chemistry and English

= (82% of 75) + (70% of 150) = 61.5 + 105 = 166.5

Total marks of Student F in Chemistry and English

= (66% of 75) + (66% of 150) = 49.5 + 99 = 148.5

∴    Reqd difference = 166.5 – 148.5 = 18
____________________________________________

Smart approach:

Reqd difference= (82 – 66)% of 75 + (70 – 66)% of 150

= 16% of 75 + 4% of 150

= 12 + 6 = 18

Hence, option C is correct.

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