# Ex.4.3 Q5 Quadratic Equations Solutions - NCERT Maths Class 10

Go back to  'Ex.4.3'

## 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.

Video Solution
Ex 4.3 | Question 5

## Text Solution

What is known?

(i) Sum of Shefali’s marks in Mathematics and English is $$30.$$

(ii) Had she got $$2$$ marks more in Mathematics and $$3$$ marks less in English, product of marks would have been $$210 .$$

What is Unknown?

Marks of Shefali in two subjects.

Reasoning:

Let the marks Shefali scored in mathematics be $$x​​​​​​​.$$

i) Then, marks scored by her in English $$\Rightarrow 30 –$$ Marks scored in Mathematics $$= 30 – x$$

ii) 2 more marks in Mathematics $$= x + 2$$

\begin{align} 3 \text{ marks less in English} &= 30-x-3\\&= 27-x \end{align}

\begin{align}\text{Product of these two }&= 210\\\left( {x + 2} \right)\left( {27 - x} \right) &= 210 \end{align}

Steps:

\begin{align}({{x}} + 2)(27 - {{x}}) &= 210\\27{{x}} - {{{x}}^2} + 54 - 2{{x}} &= 210\\ - {{{x}}^2} + 25{{x}} + 54 &= 210\\ - {{{x}}^2} + 25{{x}} + 54 - 210 &= 0\\ - {{{x}}^2} + 25{{x}} - 156 &= 0\end{align}

Multiplying both sides by $$-1:$$

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

Comparing with $$ax^\text{2}+bx+c=0$$

\begin{align} {a{\rm{ }} = 1,{b}{\rm{ }} = {\rm{ }} - 25,c{\rm{ }} = {\rm{ }}156}\\{{b^2}\rm{ }} - {\rm{ }4ac{\rm{ }} = {\rm{ }}{( - 25)^2}{\rm{ }} - {\rm{ }}4{\rm{ }}(1){\rm{ }}(156)}\\= {\rm{ }}625{\rm{ }}-{\rm{ }}624\\ = {\rm{ }}1\\ {{b^2} - {\rm{ }}4ac{\rm{ }} > {\rm{ }}0} \end{align}

\begin{align}{{x}} &= \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\\ &= \frac{{ - ( - 25) \pm \sqrt {{{( - 25)}^2} - 4(1)(156)} }}{{2(1)}}\\ &= \frac{{ - ( - 25) \pm \sqrt 1 }}{{2(1)}}\\ &= \frac{{25 \pm 1}}{2}\\x &= \frac{{25 + 1}}{2}\quad x = \frac{{25 - 1}}{2}\\x &= \frac{{26}}{2}\qquad \;x = \frac{{24}}{2}\\x &= 13 \qquad\;\; x = 12\end{align}

Two possible answers for this given question:

If Shefali scored $$13$$ mark in mathematics, then mark in English $$= \left( {30 - 13} \right) = 17.$$

If Shefali scored $$12$$ mark in mathematics, then mark in English $$= \left( {30 - 12} \right) = 18.$$

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school