Let the score of $B=100\%$
Then, the score of $A = 100\%-10\times \left(\frac{100}{100}\right)\% = 90\%$
The ratio of $A$ and $B=90\%:100\%$
- $A:B=9:10 \quad \longrightarrow (1)$
Let the score of $C=100\%$
Then the score of $B=100\%+100\times \left(\frac{25}{100}\right)\% = 125\%$
The ratio of $B$ and $C=125\%:100\%$
- $B: C=5: 4 \quad \longrightarrow (2)$
Let the score of $D=100\%$
Then the score of $C =100\%-100\times \left(\frac{20}{100}\right)\% = 80\%$
The ratio of $C$ and $D=80\%:100\%$
- $C: D=4: 5 \quad \longrightarrow (3)$
Now, from the eq$^{n} \; (2)$ and $(3)$, combining the ratios, we get
- $B: C: D = 5: 4: 5$
- $B: C: D = 10: 8: 10 \quad [\because \text{Multiply by ‘2’, for combining the ratios}]\quad \longrightarrow (4)$
Now, from the eq$^{n} \; (1)$ and $(4)$, combining the ratios, we get
- $A : B : C : D = 9 : 10 : 8 : 10$
Given that, the score of $A=72$
Let $x$ be a score of $D$. Then,
- $9 \longrightarrow 72$
- $10 \longrightarrow x$
$ \implies 9x=72\times10$
$ \implies x=80$
$\textbf{Short Method:}$
The score of $D=72 \times \left(\frac{100}{90}\right) \times \left(\frac{100}{125}\right) \times \left(\frac{100}{80}\right) = 80$
$\therefore$ The score of $D$ was $80.$
Correct Answer $:80$