In a class test, the sum of Moulika’s marks in Mathematics and English is 30. If she got 2 marks more in Mathematics and 3 marks less in English, the product of her marks would have been 210. Find her marks in the two subjects.
Answers
Answer: Her marks in mathematics and English are 12 and 18 respectively or her marks in mathematics and English are 13 and 17 respectively.
Step-by-step explanation:
Let x be the marks she got in Mathematics while y be the marks she got in English,
The sum of her marks in Mathematics and English is 30,
⇒ x + y = 30
⇒ y = 30 - x
If she got 2 marks more in Mathematics and 3 marks less in English, the product of her marks would have been 210.
⇒ (x+2) (y-3) = 210
⇒ (x+2) (30- x-3) = 210
⇒ (x+2) (27-x) = 210
⇒ 27 x + 54 - x² - 2x - 210 = 0
⇒ - x² + 25 x - 156 = 0
⇒ x² - 25 x + 156 = 0
⇒ x² - 12 x - 13 x + 156 = 0
⇒ x(x-12) - 13(x-12) = 0
⇒ (x-12) ( x-13) = 0
x = 12 or 13,
Thus,
If Her marks in mathematics = x = 12 ⇒ Her marks in English = y = 18
If Her marks in mathematics = x = 13 ⇒ Her marks in English = y = 17