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. Find her marks in the two subjects.​

Answer 1

✬ Maths = 12 or 13 ✬

✬ English = 18 or 17 ✬

Step-by-step explanation:

Given:

• Marks of Shefali in Mathematics & English is 30.
• If she got 2 marks more and 3 marks less in both subjects , then product of their marks would have been 210.

To Find:

• How many marks she got in two subjects ?

Solution: Let she got x marks in Mathematics.Therefore,

➟ Marks in English = (30 – x)

A/q

• Increasing 2 marks in Maths and decreasing 3 marks in English

• Maths = x + 2
• English = (30 – x – 3)

Now, Maths × English = 210

➯ (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 = 210 – 54

➯ 0 = x² – 25x + 156

Using middle term splitting method

➮ x² – 13x – 12x + 156

➮ x(x – 13) – 12(x – 13)

➮ (x – 13) and (x – 12)

➮ x = 13 or 12

First taking x = 12

• Marks in Maths = 12
• Marks in English = 30 – 12 = 18

Now taking x = 13

• Marks in Maths = 13
• Marks in English = 30 – 13 = 17

Answer 2

Answer:

✯ 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 :-

• What are the marks she got in two subjects.

✯ Solution :-

» Let, the marks in Mathematics be x

» So, in English the marks will be 30 - x

➣ According to the question,

⇒ (x + 2)(30 - x - 3) = 210

⇒ (x + 2)(30 - 3 - x) = 210

⇒ (x + 2)(27 - x) = 210

⇒ 27x - x² + 54 - 2x = 210

⇒ - x² + 27x - 2x + 54 - 210 = 0

⇒ - x² + 25x - 156 = 0

⇒ - (x² - 25x + 156) = 0

⇒ x² - 25x + 156 = 0

⇒ x² - (12 + 13)x + 156 = 0

⇒ x² - 12x - 13x + 156 = 0

⇒ x(x - 12) - 13(x - 12) = 0

⇒ (x - 12)(x - 13) = 0

⇒ x - 12 = 0 ; x - 13 = 0

⇒ x = 12 ; x = 13

➥ x = 12 , 13

◪ If the marks in Mathematics is 12, then the marks of English will be = 30 - 12 = 18

◩ If the marks in Mathematics is 13, then the marks of English will be = 30 - 13 = 17

$\therefore$ She got marks in Mathematics is 12 or 13 and in English is 18 or 17 .

_________________________________