Question

In an examination where full marks were 800,A gets 20% more than B,B gets 20% more than C , and C gets 15% less than D. If A got 576, what percentage of full marks did D get (approximately)?
A) 45.7
B) 51.2
C) 58.8
D) 61.7

Answer 1

Hint:First we will assume the marks of student D to be x and then according to the given conditions form the equations for marks of A,B and C and then find the value of x.
Then we will find the percentage of marks scored by D to full marks by using the formula:
\[{\text{Percentage of marks scored by D}} = \dfrac{{{\text{marks scored by D}}}}{{{\text{total marks}}}} \times 100\]

Complete step-by-step answer:
Let the marks scored by D = x
Then since it is given that C scored 15% less than D
Therefore the marks scored by C is given by:
\[{\text{marks scored by C}} = {\text{marks scored by D}} - 15\% {\text{ of marks scored by D}}\]
Hence,
\[
  {\text{marks scored by C}} = x - \dfrac{{15}}{{100}}x \\
  {\text{marks scored by C}} = x - 0.15x \\
  {\text{marks scored by C}} = 0.85x \\
 \]
Now since it is given that B scored 20% more than C
Therefore the marks scored by B is given by:
\[{\text{marks scored by B}} = {\text{marks scored by C}} + 20\% {\text{ of marks scored by C}}\]
Hence,
\[
  {\text{marks scored by B}} = 0.85x + \dfrac{{20}}{{100}}\left( {0.85x} \right) \\
  {\text{marks scored by B}} = 0.85x + 0.2\left( {0.85x} \right) \\
  {\text{marks scored by B}} = 0.85x + 0.17x \\
  {\text{marks scored by B}} = 1.02x \\
 \]
Now, since it is given that A scored 20% more than B
Therefore the marks scored by A is given by:
\[{\text{marks scored by A}} = {\text{marks scored by B}} + 20\% {\text{ of marks scored by B}}\]
Hence,
\[
  {\text{marks scored by A}} = 1.02x + \dfrac{{20}}{{100}}\left( {1.02x} \right) \\
  {\text{marks scored by A}} = 1.02x + 0.2\left( {1.02x} \right) \\
  {\text{marks scored by A}} = 1.02x + 0.204x \\
  {\text{marks scored by A}} = 1.224x...........\left( 1 \right) \\
 \]
Now since it is given that
Marks scored by A=576…………………………….(2)
Therefore equating equations 1 and 2 we get:-
\[
  1.224x = 576 \\
  x = \dfrac{{576}}{{1.224}} \\
  x = 470.5 \\
 \]
Hence the marks scored by D =470.5
Now we will calculate the percentage of marks of D using the formula:
\[{\text{Percentage of marks scored by D}} = \dfrac{{{\text{marks scored by D}}}}{{{\text{total marks}}}} \times 100\]
Putting in the known values we get:-
\[
  {\text{Percentage of marks scored by D}} = \dfrac{{470.5}}{{800}} \times 100 \\
  {\text{Percentage of marks scored by D}} = \dfrac{{470.5}}{8} \\
  {\text{Percentage of marks scored by D}} = 58.8\% \\
 \]
Hence option C is the correct option.

Note:An alternative approach to this question is:-
Since it is given that the marks scored by A=576
Also A scored 20% more than B
Therefore the marks scored by A are given by:
\[{\text{marks scored by A}} = {\text{marks scored by B}} + 20\% {\text{ of marks scored by B}}\]
Therefore,
\[
  576 = {\text{marks scored by B}} + 0.2{\text{ of marks scored by B}} \\
  576 = {\text{marks scored by B}}\left( {1 + 0.2} \right) \\
  576 = {\text{marks scored by B}}\left( {1.2} \right) \\
  {\text{marks scored by B}} = \dfrac{{576}}{{1.2}} \\
  {\text{marks scored by B}} = 480 \\
 \]
Now, since it is given that B scored 20% more than C
Therefore the marks scored by B is given by:
\[{\text{marks scored by B}} = {\text{marks scored by C}} + 20\% {\text{ of marks scored by C}}\]
Therefore,
\[
  480 = {\text{marks scored by C}} + 0.2{\text{ of marks scored by C}} \\
  480 = {\text{marks scored by C}}\left( {1 + 0.2} \right) \\
  480 = {\text{marks scored by C}}\left( {1.2} \right) \\
  {\text{marks scored by C}} = \dfrac{{480}}{{1.2}} \\
  {\text{marks scored by C}} = 400 \\
 \]
Now, since it is given that C scored 15% less than D
Therefore the marks scored by C is given by:
\[{\text{marks scored by C}} = {\text{marks scored by D}} - 15\% {\text{ of marks scored by D}}\]
Therefore,
\[
  400 = {\text{marks scored by D}} - 0.15{\text{ of marks scored by D}} \\
  {\text{400}} = {\text{ marks scored by D}}\left( {1 - 0.15} \right) \\
  {\text{400}} = {\text{ marks scored by D}}\left( {0.85} \right) \\
  {\text{marks scored by D}} = \dfrac{{400}}{{0.85}} \\
  {\text{marks scored by D}} = 470.5 \\
 \]
Now we will calculate the percentage of marks of D using the formula:
\[{\text{Percentage of marks scored by D}} = \dfrac{{{\text{marks scored by D}}}}{{{\text{total marks}}}} \times 100\]
Putting in the known values we get:-
\[
  {\text{Percentage of marks scored by D}} = \dfrac{{470.5}}{{800}} \times 100 \\
  {\text{Percentage of marks scored by D}} = \dfrac{{470.5}}{8} \\
  {\text{Percentage of marks scored by D}} = 58.8\% \\
 \]