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Question
A student obtained 60, 75 and 85 marks respectively in 3 monthly examinations in physics and 95 marks in the final examination. The 3 monthly examinations are of equal weightage whereas the final examination is weighted twice as much as monthly examination. What is his average mark physics?
82
85
79
78.75
ANSWER : 1
Descrption
<p style="margin-left:0px;">Correct option is C)</p><p>We have,</p><p style="margin-left:40px;">x<sub>1 </sub>= 60 </p><p style="margin-left:40px;">x<sub>2 </sub>=75</p><p style="margin-left:40px;">x<sub>3</sub> = 85 </p><p style="margin-left:40px;">x<sub>4 </sub>= 95 </p><p style="margin-left:40px;">w<sub>1</sub> = 1</p><p style="margin-left:40px;">w<sub>2 </sub>= 1 </p><p style="margin-left:40px;">w<sub>3</sub> = 1 </p><p style="margin-left:0px;">and w<sub>4 </sub>= 2</p><p style="margin-left:0px;"><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>x</mi><mi>w</mi></msub><mo>¯</mo></mover><mo>=</mo><mfrac><mrow><msub><mi>w</mi><mn>1</mn></msub><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><msub><mi>w</mi><mn>2</mn></msub><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>w</mi><mn>3</mn></msub><msub><mi>x</mi><mn>3</mn></msub><mo>+</mo><mo> </mo><msub><mi>w</mi><mn>4</mn></msub><msub><mi>x</mi><mn>4</mn></msub><mo></mo><mo></mo></mrow><mrow><msub><mi>w</mi><mn>1</mn></msub><mo>+</mo><msub><mi>w</mi><mn>2</mn></msub><mo>+</mo><msub><mi>w</mi><mn>3</mn></msub><mo>+</mo><msub><mi>w</mi><mn>4</mn></msub><mo></mo></mrow></mfrac></math><br>⇒ <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>x</mi><mi>w</mi></msub><mo>¯</mo></mover><mo>=</mo><mfrac><mrow><mo>(</mo><mn>1</mn><mo>×</mo><mn>60</mn><mo>)</mo><mo>+</mo><mo>(</mo><mn>1</mn><mo>×</mo><mn>75</mn><mo>)</mo><mo>+</mo><mo>(</mo><mn>1</mn><mo>×</mo><mn>85</mn><mo>)</mo><mo>+</mo><mo> </mo><mo>(</mo><mn>2</mn><mo>×</mo><mn>95</mn><mo>)</mo><mo></mo><mo></mo></mrow><mrow><mn>1</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>2</mn></mrow></mfrac></math></p><p style="margin-left:0px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mover><msub><mi>x</mi><mi>w</mi></msub><mo>¯</mo></mover><mo>=</mo><mfrac><mrow><mn>410</mn><mo></mo><mo></mo></mrow><mn>5</mn></mfrac></math></p><p style="margin-left:0px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>x</mi><mi>w</mi></msub><mo>¯</mo></mover><mo>=</mo><mn>82</mn></math></p><p style="margin-left:0px;"> </p><p style="margin-left:0px;"> </p><p style="margin-left:0px;"> </p><p style="margin-left:0px;"> </p>
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