# in a class test, the sum of the marks obtained by amit in mathematics and science is 28. she got 3 marks more in mathematics and 4 marks less in science. the product of marks obtained in two subjects is 180. find the marks obtained in the two subjects separately.

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get in a class test, the sum of the marks obtained by amit in mathematics and science is 28. she got 3 marks more in mathematics and 4 marks less in science. the product of marks obtained in two subjects is 180. find the marks obtained in the two subjects separately. from screen.

## 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.

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.

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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.

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 in mathematics be x then marks in science be 28-x

from given condition,

( x + 3 ) ( 28 − x − 4 ) = 180 ⇒ ( x + 3 ) ( 24 − x ) = 180 ⇒ 24 x − x 2 + 72 − 3 x = 180 ⇒ 21 x − x 2 − 180 + 72 = 0 ⇒ x 2 − 21 x + 108 = 0 ⇒ x 2 − 12 x − 9 x + 108 = 0 ⇒ x ( x − 12 ) − 9 ( x − 12 ) = 0 ⇒ ( x − 9 ) ( x − 12 ) = 0 ∴ x = 9 , 12

the marks scored in maths can be 9 or 12.

if she got 12 in maths then she got 28-12=16 in science

if she got 9 in maths then she got 28-9=19 in science

MathematicsSecondary School Mathematics XStandard X

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**Q.**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 him in the two subjects separately. [CBSE 2008]

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**Q.**In a class test, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in mathematics and 4 marks less in Science. The product of his marks would have been 180. Find his marks in two subjects.

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## 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

In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had ... marks obtained by him in the two subjects separately.

## 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

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## 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,

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,

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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.

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### 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 ⇒ -x2+21x+72=180 ⇒ x2-21x+180 ⇒ x2-12x+9x+108=0 ⇒ x(x-12)-9(x-12)=0 ⇒ (x-12)(x-9)=0 ⇒or x-12=0 or x-9=0 ⇒or 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.

Concept: Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated

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Chapter 10: Quadratic Equations

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RS Aggarwal Secondary School Class 10 Maths

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