Question

In an examination in which 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:
Here we will first use the conditions given to form the basic relations between them. Then we will put the value of the marks of A in these conditions to get the value of the marks of the others. Then we will divide the marks of D with the full marks and multiply it by 100 to get the percentage of full marks that D gets.

Complete Step by step Solution:
It is given that the full marks were 800.
Firstly we will write all the given information in the equation form. Therefore, we get
\[\begin{array}{l}A = \dfrac{{120}}{{100}}B = \dfrac{6}{5}B\\B = \dfrac{{120}}{{100}}C = \dfrac{6}{5}C\\C = \dfrac{{85}}{{100}}D = \dfrac{{17}}{{20}}D\end{array}\]
It is given that if A got 576. Then by using this we will calculate the marks of the rest. Therefore, we get
We know that \[A = \dfrac{6}{5}B\], putting the value of A in this we will get the value of B, we get
\[576 = \dfrac{6}{5}B\]
On cross multiplication, we get
\[ \Rightarrow B = \dfrac{5}{6} \times 576\]
Dividing the terms, we get
\[ \Rightarrow B = 5 \times 96 = 480\]
Now we will put the value of B in the equation \[B = \dfrac{6}{5}C\] to get the value of C. Therefore, we get
\[480 = \dfrac{6}{5}C\]
On cross multiplication, we get
\[ \Rightarrow C = \dfrac{5}{6} \times 480\]
Dividing the terms, we get
\[ \Rightarrow C = 5 \times 80 = 400\]
Now we will put the value of C in the equation \[C = \dfrac{{17}}{{20}}D\] to get the value of D. Therefore, we get
\[400 = \dfrac{{17}}{{20}}D\]
On cross multiplication, we get
\[ \Rightarrow D = \dfrac{{20}}{{17}} \times 400\]
Multiplying the terms, we get
\[ \Rightarrow D = \dfrac{{8000}}{{17}}\]
Now we will divide the marks by D with the total marks and multiply it with 100 to get the percentage of full marks that D get
Percentage of full marks that D get \[ = \dfrac{{\dfrac{{8000}}{{17}}}}{{800}} \times 100 = 58.82\% \]
Hence, the percentage of full marks that D gets is \[58.82\% \].

So, option C is the correct option.

Note:
The percentage of a variable is equal to the ratio of the value of the variable to the total value of the variable and multiplied by 100 to get the required percentage of the variable. The percentage can be represented in the decimal as well as fraction. In real life, we use the percentage to represent the marks obtained in an exam, etc.