Question

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.​

Answer 1

Let Shefalis's marks in Mathematics be x and in English be y

According to the problem ,

$x + 2 + y - 3 = 30$

Let above equation be no(i)

Again ATP,

$xy = 210$

Let this be equation be no (ii)

$x = \frac{210}{y}$

Substituting the value of of x in equation i we get,

$x + 2 + y - 3 = 30 \\ = > x - 1 + y = 30 \\ = > x + y = 31 \\ = > \frac{210}{y} + y = 31\\ = > \frac{210 + {y}^{2} }{y} = 31 \\ = > 210 + {y}^{2} = 31y \\ = > 210 + {y}^{2} - 31y = 0 \\ = > {y}^{2} - 31</u><u>y</u><u> + 210 = 0 \\ = > {y}^{2} - (21 + 10) y+ 210 = 0 \\ {y}^{2} - 21y - 10y + 210 = 0 \\ = > y(y - 21) - 10(y - 21) = 0 \\ y - 10 = 0 \\ y - 21 = 0 \\ y = 10 \\ y = 21$

Substituting the value of y=10 and y=21 in equation ii we get

$xy = 210 \\ = > x(10) = 210 \\ = > x = 21$

Again

$x(21) = 210 \\ = > x = 10$

Therfore

In mathematics he got

x+2

=12

and in English he got =30-12

18

Answer 2

Answer:

Let us say, the marks of Shefali in Maths be x.

Then, the marks in English will be 30 – x.

As per the given question,

(x + 2)(30 – x – 3) = 210

(x + 2)(27 – x) = 210

⇒ -x^2 + 25x + 54 = 210

⇒ x^2 – 25x + 156 = 0

⇒ x^2 – 12x – 13x + 156 = 0

⇒ x(x – 12) -13(x – 12) = 0

⇒ (x – 12)(x – 13) = 0

⇒ x = 12, 13

Therefore,

if the marks in Maths are 12,

then marks in English will be 30 – 12 = 18

and the marks in Maths are 13,

then marks in English will be 30 – 13 = 17.