Advertisements
Advertisements
Question
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.
Solution
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.
APPEARS IN
RELATED QUESTIONS
Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.
Divide two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.
300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.
In a class test, the sum of Kamal’s marks in mathematics and English is 40. Had he got 3 marks more in mathematics and 4 marks less in English, the product of the marks would have been 360. Find his marks in two subjects separately.
A dealer sells an article for ₹ 75 and gains as much percent as the cost price of the article. Find the cost price of the article.
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hr more, it would have taken 30 minutes less for the journey. Find the original speed of the train.
A motor boat whose speed in still water is 178 km/hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream
The length of a rectangular field is three times its breadth. If the area of the field be 147 sq meters, find the length of the field.
A car moves a distance of 2592 km with uniform speed. The number of hours taken for the journey is one-half the number representing the speed, in km/hour. Find the time taken to cover the distance.
Write a quadratic polynomial, sum of whose zeros is \[2\sqrt{3}\] and their product is 2.
