Direction: Study the data carefully and answer the questions given beside:
 
The table shows the percentage of marks obtained by five students in five different subjects and some data is missing.
 
   Maths 
 (100)
 English 
(150)
 Hindi 
(80)
 Commerce 
(160)
Art
 (125) 
Chintu - 40% - 65% 56%
 Sheena  - 68% 85% - 76%
Umesh 62% - 90% 70% -
 Aryansh  88% 70% - - 84%
Himani 78% - 75% 85% -

Important for :
1
If the overall percentage of marks obtained by Umesh in all the subjects is 80% and the marks obtained by Umesh in English is 26 marks more than the marks obtained by Umesh in Art, find the percentage of marks obtained by Umesh in Art.
» Explain it
D
Total maximum marks = 100 + 150 + 80 + 160 + 125 = 615 marks

Overall marks obtained by Umesh = 615 × 80% = 492

Let Marked obtained in Art = x, English = x + 26

According to the question,

100 × 62% + x + 26 + 80 × 90% + 160 × 70% + x = 492

62 + x + 26 + 72 + 112 + x = 492

2x + 272 = 492

2x = 492 – 272

2x = 220

x = 110

Marks obtained by Umesh in Art = 110

% = 110/ 125 × 100 = 88%

Hence, option D is correct.

2
What is the ratio of the marks obtained by Chintu in English and Commerce together to the marks obtained by Aryansh in English and Art together.
» Explain it
D
Marks obtained by Chintu in English = 150 × 40% = 60

Marks obtained by Chintu in Commerce = 160 × 65% = 104 

Marks obtained by Aryansh in English = 150 × 70% = 105

Marks obtained by Aryansh in Art = 125 × 84% = 105

Ratio = 60 + 104 : 105 + 105

= 164 : 210

= 82 : 105

Hence, option D is correct.

3
If the total marks obtained by Sheena in English, Hindi and Commerce is 290 and the total marks obtained by Himani in Math, Hindi and Art is 218, find the difference between the marks obtained by Sheena in Commerce and the marks obtained by Himani in Art.
» Explain it
B
Marks obtained by Sheena in English = 150 × 68% = 102

Marks obtained by Sheena in Hindi = 80 × 85% = 68

Marks obtained by Sheena in Commerce = 290 – 102 – 68 = 120

Marks obtained by Himani in Math = 100 × 78% = 78

Marks obtained by Himani in Hindi = 80 × 75% = 60

Marks obtained by Himani in Art = 218 – 78 – 60 = 80

Difference = 120 – 80 = 40 marks

Hence, option B is correct.

4
If the marks obtained by Umesh in English is 90 and the marks obtained by Himani in English is 114, find the percentage of marks obtained by all students in English.
» Explain it
C
Marks obtained by Chintu in English = 150 × 40% = 60

Marks obtained by Sheena in English = 150 ​× 68% = 102

Marks obtained by Umesh in English = 90

Marks obtained by Aryansh in English = 150 ​× 70% = 105

Marks obtained by Himani in English = 114

Total marks = 60 + 102 + 90 + 105 + 114 = 471

Total maximum marks = 150 × 5 = 750

% = 471/ 750 × 100 = 62.8%

Hence, option C is correct.

5
Marks obtained by Aryansh in Math and Art together is approximately how much percentage more than the marks obtained by Himani in Commerce?
» Explain it
E
Marks obtained by Aryansh in Math = 100 × 88% = 88

Marks obtained by Aryansh in Art = 125 × 84% = 105

Marks obtained by Himani in Commerce = 160 × 85% = 136

% more =  105 + 88 – 136  × 100
136

57  × 100 = 41.9% ≈ 42%
136

Hence, option E is correct.