Answer
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Hint: The relation between the marks of A, B, C and D are given in the question. Start with formulating equations to get numerical relation between them as the overall marks of A is given. Use this concept to get D’s percentage.
Complete Step-by-Step solution:
Total marks were = 800.
Now it is given that A got 576 marks.
Now again it is given that A gets 20% more than B.
So construct the linear equation according to this information we have,
Therefore marks of A = B + 20%B
$ \Rightarrow A = B + \dfrac{{20}}{{100}}B = 1.2B$
$ \Rightarrow B = \dfrac{A}{{1.2}} = \dfrac{{576}}{{1.2}} = 480$
Now again it is given that B gets 20% more than C.
So construct the linear equation according to this information we have,
Therefore marks of B = C + 20%C
$ \Rightarrow B = C + \dfrac{{20}}{{100}}C = 1.2C$
$ \Rightarrow C = \dfrac{B}{{1.2}} = \dfrac{{480}}{{1.2}} = 400$
Now again it is given that C gets 15% less than B.
So construct the linear equation according to this information we have,
Therefore marks of C = D - 15%B
$ \Rightarrow C = D - \dfrac{{15}}{{100}}D = 0.85D$
$ \Rightarrow D = \dfrac{C}{{0.85}} = \dfrac{{400}}{{0.85}}$
So the percentage of marks D gets is the ratio of marks D got to the total marks multiplied by 100.
$ \Rightarrow D = \dfrac{{\dfrac{{400}}{{0.85}}}}{{800}} \times 100 = \dfrac{{100}}{{2 \times 0.85}} = \dfrac{{100}}{{1.7}} = 58.8$ %
So this is the required percentage of full marks D get approximately.
Hence option (C) is correct.
Note: Whenever we face such types of problems the key point is that although marks of a candidate are given but however the data asked is in terms of percentage. So use the basic concept of percentage to get everything in percentage during formulation of equations.
Complete Step-by-Step solution:
Total marks were = 800.
Now it is given that A got 576 marks.
Now again it is given that A gets 20% more than B.
So construct the linear equation according to this information we have,
Therefore marks of A = B + 20%B
$ \Rightarrow A = B + \dfrac{{20}}{{100}}B = 1.2B$
$ \Rightarrow B = \dfrac{A}{{1.2}} = \dfrac{{576}}{{1.2}} = 480$
Now again it is given that B gets 20% more than C.
So construct the linear equation according to this information we have,
Therefore marks of B = C + 20%C
$ \Rightarrow B = C + \dfrac{{20}}{{100}}C = 1.2C$
$ \Rightarrow C = \dfrac{B}{{1.2}} = \dfrac{{480}}{{1.2}} = 400$
Now again it is given that C gets 15% less than B.
So construct the linear equation according to this information we have,
Therefore marks of C = D - 15%B
$ \Rightarrow C = D - \dfrac{{15}}{{100}}D = 0.85D$
$ \Rightarrow D = \dfrac{C}{{0.85}} = \dfrac{{400}}{{0.85}}$
So the percentage of marks D gets is the ratio of marks D got to the total marks multiplied by 100.
$ \Rightarrow D = \dfrac{{\dfrac{{400}}{{0.85}}}}{{800}} \times 100 = \dfrac{{100}}{{2 \times 0.85}} = \dfrac{{100}}{{1.7}} = 58.8$ %
So this is the required percentage of full marks D get approximately.
Hence option (C) is correct.
Note: Whenever we face such types of problems the key point is that although marks of a candidate are given but however the data asked is in terms of percentage. So use the basic concept of percentage to get everything in percentage during formulation of equations.
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