Question

Priya got 9 marks more in History than
what she got in Geography. Her History
marks are 56% of the sum of her History
and Geography marks. What are her
Geography marks?​

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \star \: \text{ \pink{Geography marks are more than history}} \\ \text{ \pink{ by 9 marks.}} \\ \\ \star \: \text{ \pink{History marks are 50 \% of the sum of }} \\ \text{ \pink{the history and geography marks. }} \\ \\ \\ \underline{ \mathfrak{ \: \: To \: \: find : \to \: \: }} \\ \\ \: \: \: \: \star \: \text{ \pink{The geography marks = ?}}$

$\mathfrak{Suppose,} \\ \\ \text{ \red{The marks of geography = x }} \\ \\ \text{ \red{The marks of history = x + 9}}\\ \\ \text{ \blue{Sum of the marks of geography and}} \\ \text{ \blue{ history = x + ( x + 9 ) }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \text{ \blue{= x + x + 9}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \text{ \blue{= 2x + 9}}$

$\tt{56\% \: \: of \: \: the \: \: sum = 56\% \: \: of \: \: ( 2x + 9 ) } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = \frac{56}{100} \times (2x +9 ) } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = \frac{14}{25} (2x + 9)}$

$\tt{ \therefore \: History \: \: marks = \frac{14}{25} (2x + 9)} \\ \\ \tt{ \implies \: x + 9 = \frac{14}{25}(2x + 9) } \\ \\ \tt{ \implies \:25(x + 9) = 14(2x + 9)} \\ \\ \tt{ \implies \:25x + 225 = 28x + 126} \\ \\ \tt{ \implies \:25x - 28x = 126 - 225} \\ \\ \tt{ \implies \: - 3x = - 99} \\ \\ \tt{ \implies \:3x = 99} \\ \\ \tt{ \implies \:x = \frac{99}{3} } \\ \\ \: \: \: \: \: \: \: \: \tt{ \therefore \: \: x = 33}$

$\red{ \bold{ \therefore \: \: Geography \: \: \: marks, x = \underline{ \: 33 \: }}}$