In a class test the sum of shefali mark in maths and english is 30 she had got two marks more in mathematics and 3 marks less in english the product of their marks could have been 210 find the marks in the two subjects
Answers
total 30marks
we can divide into 2halfs means
17.5+12=30
17.5×12=210
here in maths 2marks high and in english 3marks less
so it is simple to say the answer is 17.5 and 12
GIVEN:
- Sum of shefali mark in maths and english is 30.
- If she had got two marks more in mathematics and 3 marks less in english the product of their marks could have been 210.
TO FIND:
- Marks scored by her in two subjects.
SOLUTION:
Let 'x' be the marks scored in mathematics.
Let 'y' be the marks scored in English.
Case 1
=> x+y = 30.
=> x = 30-y ....(i)
Case 2
=> (x+2)(y-3) = 210
=> xy-3x+2y-6 = 210
=> xy-3x+2y = 216 ....(ii)
Putting x = 30-y in eq(ii)
=> (30-y)y-3(30-y)+2y = 216.
=> 30y-y²-90+3y+2y = 216
=> -y²+35y-90-216 = 0
=> -y²+35y-306 = 0
=> -(y²-35y+306) = 0
=> y²-35y+306 = 0
=> y²-17y-18y+306 = 0
=> y(y-17)-18(y-17) = 0
=> (y-17)(y-18) = 0
Either y-17 = 0.
=> y = 17
Putting y = 17 in eq(i)
=> x = 30-17
=> x = 13
Marks scored in English = 17.
Marks scored in mathematics = 13
Either y-18 = 0
=> y = 18.
Putting y = 18 in eq(i)
=> x = 30-18
=> x = 12
Marks scored in English = 18.
Marks scored in mathematics = 12.