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प्रश्न
In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained by him in the two subjects separately.
उत्तर
Let the marks obtained by P in mathematics and science be x and (28- x) respectively. According to the given condition,
`(x+3)(28-x-4)=180`
⇒`(x+3) (24-x)=180`
⇒`-x^2+21x+72=180`
⇒`x^2-21x+180`
⇒`x^2-12x+9x+108=0`
⇒`x(x-12)-9(x-12)=0`
⇒`(x-12) (x-9)=0`
⇒`x-12=0 or x-9=0`
⇒`x=12 or x=9`
When `x=12`
`28-x=28-12=16`
When `x=9`
`28-x=28-9=19`
Hence, he obtained 12 marks in mathematics and 16 marks in science or 9 marks in mathematics and 19 marks in science.
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