Had Ajita scored 10 more marks in her mathematics test out of 30 marks

1.	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» Let her actual marks be x Therefore, 9 (x +10) = x² i.e., x² – 9x – 90 = 0 i.e., x² – 15x + 6x – 90 = 0 i.e., x(x – 15) + 6(x –15) = 0 i.e., (x + 6) (x –15) = 0 Therefore, x = – 6 or x = 15 Since x is the marks obtained, x ≠ – 6. Therefore, x = 15. So, Ajita got 15 marks in her mathematics test.

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»

Let her actual marks be x

Therefore, 9 (x +10) = x²

i.e., x² – 9x – 90 = 0

i.e., x² – 15x + 6x – 90 = 0

i.e., x(x – 15) + 6(x –15) = 0

i.e., (x + 6) (x –15) = 0

Therefore, x = – 6 or x = 15

Since x is the marks obtained, x ≠ – 6. Therefore, x = 15.

So, Ajita got 15 marks in her mathematics test.