In a class test, the sum of 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 in two subjects separately.
Answers
Step-by-step explanation:
Given :-
In a class test, the sum of 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?
To find:-
Find the marks obtained in two subjects separately.
Solution:-
Let the marks obtained by P in mathematics be X
Let the marks obtained by P in Science be Y
the sum of marks obtained by P in Mathematics and Science is 28.
X+Y = 28 ---------(1)
and X = 28-Y ------(2)
he got 3 more marks in Mathematics then
the marks = X+3
and 4 marks less in Science then
the marks = Y-4
the product of marks obtained in the two subjects would have been 180
=>(X+3)×(Y-4) = 180-------(3)
On Substituting the value of X in (3) then
=>(28-Y+3)×(Y-4) = 180
=>(31-Y)×(Y-4) = 180
=>31Y -124 - Y^2 + 4Y = 180
=>-Y^2 + 35Y -124 = 180
=>-Y^2 + 35Y -124 - 180 = 0
=>-Y^2 + 35Y -304 = 0
=> Y^2 - 35Y + 304 = 0
=> Y^2 -16Y -19Y +304 = 0
=> Y(Y -16) -19 (Y-16) = 0
=>(Y - 16) (Y - 19) = 0
=>Y - 16 = 0 (or) Y - 19 = 0
=>Y = 16 and 19
On Substituting the value of Y = 16 in (1)
=>X+16 = 28
=>X = 28 - 16
=>X = 12
On Substituting the value of Y = 19 in (1)
=>X+19 = 28
=>X = 28 - 19
=>X = 9
Therefore, Marks in mathematics =12 or 9
Marks in Science = 16 or 19
Answer:-
He got Marks in mathematics = 12 or 9
He got marks in Science = 16 or 19
Check:-
1) Marks in mathematics = 12
Marks in Science = 16
Their sum = 12+16 = 28
and
he got 3 more marks in Mathematics = 12+3 = 15
4 marks less in Science= 16-4 = 12
Their product = 15×12 = 180
Verified the given relations
2) Marks in mathematics = 9
Marks in Science = 19
Their sum = 9+19 =28
he got 3 more marks in Mathematics = 9+3=12
marks less in Science = 19-4 = 15
Their product = 12×15 = 180
Verified the given relations