5. In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Answers
Question :
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210.
To Find :
Find her marks in the two subjects.
Let us assume :
The marks in Mathematics be x ---------(1)
Hence, according to the situation
Marks in English be 30 - x ----------(2)
Solution :
According to the question we know :
- Shefali got 2 marks more in Mathematics = x + 2
(Note : We got x from (1) to find the marks in Mathematics)
- She got 3 marks less in English = 30 - x - 3
(Note : We got 30 - x from (2) and 3 from the given data)
The product of their marks is 210 which means : (x + 2)(30 - x - 3) = 210
Hence, solving this equation we will find x
→ (x + 2)(30 - x - 3) = 210
→ (x + 2)(27 - x) = 210
By simplifying (x + 2)(27 - x) we get
→ x(27 - x) + 2(27 - x) = 210
→ 27x - x² + 54 - 2x = 210
→ 25x - x² = 210 - 54 = 210
→ 25x - x² = 156
→ x² - 25x + 156 = 0
Now to split the middle term by middle term factorisation
→ x² - (13 + 12)x + 156 = 0
→ x² - 13x - 12x + 156 = 0
Now to take the common
→ x(x - 13) - 12(x - 13) = 0
Taking (x - 13) as common we get
→ (x - 13)(x - 12) = 0
Now we can write that,
x - 13 = 0
- x = 13
x - 12 = 0
- x = 12
So from the above we got two conditions
First Condition :
If x = 13
We get marks in Maths as 13
English : 30 - x = 30 - 12 → 17
THEREFORE
- Maths = 13 marks
- English = 17 marks
For the second condition :
If x = 12
We get marks in Maths as 12
English : 30 - x = 30 - 12 → 18
HENCE
- Maths = 12 marks
- English = 18 marks
Regards
# BeBrainly
ANSWER:
- Shefali's marks in two subjects (Mathematics, English) can be (12,18) or (13,17).
GIVEN:
- In a class test, the sum of Shefali’s marks in Mathematics and English is 30.
- Had she got 2 marks more in Mathematics and 3 marks less in English.
- The product of their marks would have been 210.
TO FIND:
- Her marks in the two subjects.
SOLUTION:
Let the marks of Shefali in Mathematics be x, then in English it will be 30 - x since the sum of Mathematics and English marks is 30.
Given that :
- She got 2 marks more in Mathematics and 3 marks less in English.
- The product of their marks would have been 210.
That is :
- (Mathematics marks + 2) × (English marks - 3) = 210
- (x + 2) × (30 - x - 3) = 210
Solving the equation we get,
⇒ (x + 2) (30 - x - 3) = 210
⇒ (x + 2) (27 - x) = 210
⇒ x(27 - x) + 2(27 - x) = 210
⇒ 27x - x² + 54 - 2x = 210
⇒ 25x - x² + 54 = 210
⇒ x² - 25x + 156 = 0
Splitting the middle term,
⇒ x² - 25x + 156 = 0
⇒ x² - 12x - 13x + 156 = 0
⇒ x(x - 12) - 13(x - 12) = 0
⇒ (x - 12) (x - 13) = 0
⇒ x = 12 & x = 13
If x = 12,
⇒ Mathematics marks (x) = 12
⇒ English marks (30 - x) = 18
If x = 13,
⇒ Mathematics marks (x) = 13
⇒ English marks (30 - x) = 17
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