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A student scored a total of $32$ marks in class tests in Mathematics and Science. Had he scored $2$ marks less in Science and $4$ marks more in Mathematics, the product of his marks would have been $253$. Find his marks in the two subjects.
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Let marks scored in Mathematics be $x$
and marks scored in Science be $y$
ATQ,
$x + y = 32$ ..............(i) (1)
and $(x + 4)(y - 2) = 253$ ...... (ii) (1)
from (i) and (ii)
$x^2 - 26x + 133 = 0$ (1)
$(x - 19)(x - 7) = 0$ (1)
$x = 19, 7$ (1/2)
$x = 19 \Rightarrow y = 13$
$x = 7 \Rightarrow y = 25$ (1/2)
Hence, marks in Mathematics and Science are $19, 13$ or $7, 25$
and marks scored in Science be $y$
ATQ,
$x + y = 32$ ..............(i) (1)
and $(x + 4)(y - 2) = 253$ ...... (ii) (1)
from (i) and (ii)
$x^2 - 26x + 133 = 0$ (1)
$(x - 19)(x - 7) = 0$ (1)
$x = 19, 7$ (1/2)
$x = 19 \Rightarrow y = 13$
$x = 7 \Rightarrow y = 25$ (1/2)
Hence, marks in Mathematics and Science are $19, 13$ or $7, 25$