Question

In a test, Vivek secured 4 marks more in
Marathi than the marks he secured in Maths.
9 times of the marks he secured in Marathi is
equal to the square of the marks in Maths.
Find his marks in Marathi and Maths in a test.​

Answer 1

Given :

• First condition

Vivek secured 4 marks more in Marathi than the marks he secured in Maths.

• Second condition

9 times of the marks he secured in Marathi is equal to the square of the marks in Maths.

To find :

• Marks obtained in Marathi & Maths in a test.

Solution :

• According to the first condition

Vivek secured 4 marks more in Marathi than the marks he secured in Maths.

Consider the marks in maths be x

→ Marathi = x + 4

• According to the second condition

9 times of the marks he secured in Marathi is equal to the square of the marks in Maths.

→ 9×(Marks in Marathi) = (Marks in maths)²

→ 9 × (x + 4) = (x)²

→ 9x + 36 = x²

→ x² - 9x - 36 = 0

• Split middle term

→ x² - 12x + 3x - 36 = 0

→ x(x - 12) + 3(x - 12) = 0

→ (x + 3)(x - 12) = 0

Either

→ (x + 3) = 0

→ x = - 3

Or

→ (x - 12) = 0

→ x = 12

• Take x = 12 & ignore x = - 3

Put the value of x in Marathi

→ (x + 4)

→ 12 + 4

→ 16

•°• Marks in Marathi & Maths are 16 & 12 respectively.

━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

Given :-

In test, Vivek secured 4 marks more in

Marathi than the marks he secured in Maths.

9 times of the marks he secured in Marathi is

equal to the square of the marks in Maths.

To Find :-

Marks in Marathi and Maths test

Solution :-

Let the marks in maths be l

and Mark in Marathi will be l + 4

Since,

When Marathi marks is 9 times greater than square of maths

$\bf 9( \ell + 4) = {( \ell) }^{2}$

$\bf \:9 \ell + 36 = { \ell}^{2}$

$\bf \: { \ell}^{2} - 9 \ell - 36 = 0$

$\bf \: { \ell}^{2} - (12 \ell - 3 \ell) - 36 = 0$

$\bf \: { \ell}^{2} - 12 \ell + 3 \ell - 36 = 0$

$\bf \ell( \ell - 12) \: + \: 3( \ell - 12) = 0$

$\bf( \ell + 3) \: or( \ell - 12)$

$\ell = - 3$

or

$\ell = 12$

Negative Value can't be accepted. Therefore

$\ell = 12$

Marks in Marathi

$\bf \ell + 4 = 12 + 4 = 16$