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 find the marks obtained by D then find the percentage required and to find the marks of D we have to find the marks of C and to find the marks of C we have to find the marks of B.

Complete step by step solution:
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 $576$.
We have to find the percentage of full marks D did get.
As A gets $20\% $ more than B so we make an equation here.
$
  {\text{A = 120% }}\,{\text{of}}\,{\text{B}} \\
  {\text{A = }}\dfrac{{120}}{{100}} \times {\text{B}} \\
$
$\dfrac{{5{\text{A}}}}{6} = {\text{B}}$ --equation $\left( 1 \right)$
As B gets $20\% $ more than C so we make another equation here
$
  {\text{B = 120% }}\,{\text{of C}} \\
  {\text{B = }}\dfrac{{120}}{{100}} \times {\text{C}} \\
$
$\dfrac{5}{6}{\text{B = C}}$ --equation$\left( 2 \right)$
As C gets $15\% $ less than D, so we make another equation here.
$
  {\text{C = 85% }}\,{\text{of D}} \\
  {\text{C = }}\dfrac{{85}}{{100}} \times {\text{D}} \\
$
$\dfrac{{20{\text{C}}}}{{17}} = {\text{D}}$ --equation$\left( 3 \right)$
In question it is given that A got $576$ marks therefore we put this value in equation $\left( 1 \right)$
$
  \dfrac{{5{\text{A}}}}{6} = {\text{B}} \\
  \dfrac{5}{6} \times 576 = {\text{B}} \\
  {\text{480 = B}} \\
$
So B has got $480$ marks so we put the value of B in equation $\left( 2 \right)$
$
  \dfrac{5}{6} \times 480 = {\text{C}} \\
  400 = {\text{C}} \\
$
So C has got $400$ marks now will put this value in equation $\left( 3 \right)$
$
  \dfrac{{20}}{{17}} \times 400 = {\text{D}} \\
  \dfrac{{8000}}{{17}} = {\text{D}} \\
$
So D has got $\dfrac{{8000}}{{17}}$ marks.
Now we will find the percentage of full marks did D get.
As total marks $ = 800$
Marks D has got $ = \dfrac{{8000}}{{17}}$
Hence, required percentage $ = \left( {\dfrac{{\dfrac{{8000}}{{17}}}}{{800}} \times 100} \right)$
$
   = \dfrac{{8000 \times 100}}{{800 \times 17}} \\
   = \dfrac{{1000}}{{17}} \\
   = 58.8\% \\
$
So D has got $58.8\% $ of full marks.
Note: We have applied here the formula of percentage which is required percentage $ = \dfrac{{{\text{No}}{\text{.}}\,{\text{of}}\,{\text{marks}}\,{\text{obtained}}}}{{{\text{total}}\,{\text{no}}{\text{.}}\,{\text{of}}\,{\text{marks}}}} \times 100$ to find the required percentage and we have found here the no. of marks obtained by D and total no. of marks are given.