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**.**

A natural number when increased by 12 equals 160 times its reciprocal. Find the number.

Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is \( \dfrac{29}{20}\) Find the original fraction.

The sum of the squares of two consecutive even numbers is 340. Find the numbers.

The sum of the squares of two consecutive multiple of 7 is 637. Find the multiples.