Question : Two students appeared for an examination. One of them secured 19 more marks than the other and his marks were 60% of the sum of their marks. The marks obtained by them are:
Option 1: 78 and 59
Option 2: 57 and 38
Option 3: 45 and 26
Option 4: 99 and 80
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Correct Answer: 57 and 38
Solution :
Let one of them get $x$ marks.
Then the other one gets ($x + 19)$ marks.
According to the question,
$x + 19 = (x + x + 19) × \frac{60}{100}$
⇒ $x + 19 = (2x+ 19) × \frac{3}{5}$
⇒ $5(x + 19) = 3(2x + 19)$
⇒ $5x + 95 = 6x + 57$
$\therefore x = 38$
So, one got 38 and the other got (38 + 19) = 57
Hence, the correct answer is 57 and 38.
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