Question

Q. Had Ajita scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?

Answer 1

Answer: 15 Marks

Solution:

Let Ajita had scored x marks in the test of Mathematics.

According to the question,If she scored 10 marks more=> x+10

then 9 times of the marks = square of actual marks

So

$9(10 + x) = {x}^{2} \\ \\ {x}^{2} - 9x - 90 = 0 \\ \\ {x}^{2} - 15x + 6x - 90 = 0 \\ \\ x(x - 15) + 6(x - 15) = 0 \\ \\ (x - 15)(x + 6) = 0 \\ \\ so \\ \\ x - 15 = 0 \\ \\ x = 15 \\ \\ or \\ \\ x + 6 = 0 \\ \\ x = - 6$
Neglect x = -6

So, marks that Ajita scored are = 15

Verification:

$= 9(15 + 10) \\ \\ = 9 \times 25 \\ \\ = > 225 = ( {15)}^{2} = 225$

Answer 2

Answer:

15

Solution:

Let Ajita had scored x marks in the test of Mathematics.

According to the question,If she scored 10 marks more=> x+10

then 9 times of the marks = square of actual marks

So

\begin{lgathered}9(10 + x) = {x}^{2} \\ \\ {x}^{2} - 9x - 90 = 0 \\ \\ {x}^{2} - 15x + 6x - 90 = 0 \\ \\ x(x - 15) + 6(x - 15) = 0 \\ \\ (x - 15)(x + 6) = 0 \\ \\ so \\ \\ x - 15 = 0 \\ \\ x = 15 \\ \\ or \\ \\ x + 6 = 0 \\ \\ x = - 6 \\ \\\end{lgathered}

9(10+x)=x

2

x

2

−9x−90=0

x

2

−15x+6x−90=0

x(x−15)+6(x−15)=0

(x−15)(x+6)=0

so

x−15=0

x=15

or

x+6=0

x=−6

Neglect x = -6

So, marks that Ajita scored are = 15

Verification:

\begin{lgathered}= 9(15 + 10) \\ \\ = 9 \times 25 \\ \\ = > 225 = ( {15)}^{2} = 225 \\\end{lgathered}

=9(15+10)

=9×25

=>225=(15)

2

=225