from a handpicked tutor in LIVE 1-to-1 classes

# 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

**Solution:**

Let the marks scored by Shefali in mathematics be x.

Then, marks scored by her in English = 30 - Marks scored in Mathematics = 30 - x

Let us add 2 more marks in Mathematics = x + 2

Let us reduce English by 3 marks = 30 - x - 3 = 27 - x

According to the given question, Product of these two marks = 210

(x + 2) (27 - x) = 210

27x - x^{2} + 54 - 2x = 210

- x^{2} + 25x + 54 = 210

- x^{2} + 25x + 54 - 210 = 0

- x^{2} + 25x - 156 = 0

On multiplying both sides by -1, we get

x^{2} - 25x + 156 = 0

Now we will use middle term factorisation to solve further.

x^{2} - 12x - 13x + 156 = 0

(x - 12) (x - 13) = 0

x = 13 and x = 12

Two possible answers for this given question is:

If Shefali scored 13 mark in mathematics, then marks scored in English = (30 - 13) = 17.

If Shefali scored 12 mark in mathematics, then marks scored in English = (30 - 12) = 18.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 4

**Video Solution:**

## 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

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.3 Question 5

**Summary:**

If in a class test, the sum of Shefali’s marks in Mathematics and English is 30 and had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210, then Shefali's marks in the two subjects are 12 in mathematics and 18 marks in English or 13 in mathematics and 17 marks in English.

**☛ Related Questions:**

- The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the fields.
- The difference of squares of two numbers is 180. The square of a smaller number is 8 times the larger number. Find the two numbers.
- A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.
- Two water taps together can fill a tank in 9 3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank?

visual curriculum