Question

In an examination, Ramya got 9 marks less than twice that of Udaya. Product of their marks is 195.Who got more marks? How much?

Answer 1

Hint:In the examination, Ramya got 9 marks less than twice that of Udaya got.So, we will first take in the examination Udaya got x marks (a random number).Then by given condition we can find the marks of Ramya.As the product of their marks is 195 is given, we can easily find an equation in terms of x.Solving the equation, we can find the value of x.Then evaluating Ramya’s marks, we can see who got more marks and how much.


Complete step-by-step answer:
It is given that, in the examination, Ramya got 9 marks less than twice that of Udaya.
Let, Udaya’s marks in the examination = x
Then Ramya got the marks = 2x-9
Also given that, the product of Ramya and Udaya’s marks is 195.
So, Ramya’s marks × Udaya’s marks = 195
\[\left( {2x - 9} \right) \times x = 195\]
\[2{x^2} - 9x = 195\]
\[2{x^2} - 9x - 195 = 0\]
Solving the quadratic equation by Sridharacharya’s formula we get,
\[x = \dfrac{{ - ( - 9) \pm \sqrt {81 - ( - 4 \times 2 \times 195} )}}{{2 \times 2}}\]
Let us solve the terms in the above form, we get,
\[x = \dfrac{{9 \pm \sqrt {81 + 1560} }}{4}\]
\[x = \dfrac{{9 \pm \sqrt {1641} }}{4}\]
By finding the value of root we get,
\[x = \dfrac{{9 \pm 40.50}}{4}\]
Writing it as two terms we get,
\[x = \dfrac{{9 + 40.50}}{4}or,\dfrac{{9 - 40.50}}{4}\]
\[x = 12.37\] $\text{or}$ \[- 7.875\]
We can’t take the negative value since marks cannot be negative, so Udaya’s marks in the examination is 12.37
Then Ramya’s marks in the examination is found by substituting the value of x in equation (1)
2x-9 = (2×12.37)-9 = 15.74
The difference between Ramya and Udaya’s marks is = (15.74-12.37) = 3.37 marks.
Hence, Ramya got more marks and Ramya got 3.37 marks more than Udaya.

Note:Sridharacharya’s formula to solve quadratic equation
\[a{x^2} + bx + c = 0\] is \[x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]
Here we do not take the negative value of x since marks obtained by a person cannot be negative.Students should remember this formula for solving these types of questions.