Question

In a class test sum of shefali's marks in mathematics and English is 30. Had she got 2 mark more in mathematics and 3marks less in English. The product of the marks would have been 210. Find her marks in 2 subjects.

Answer 1

$\small{\sf{\:\:\:\:\:\:\:\:\:\:\:\: Assumption}}$

Let us assume that Shefali got M marks in Maths.

In a class test sum of shefali's marks in mathematics and English is 30.

$\implies$ Marks in English = 30 - M

Also, she got 2 mark more in mathematics and 3 marks less in English.

The product of the marks would have been 210.

$\implies\:\sf{(M+2)(30-M-3)\:=\:210}$

$\implies\:\sf{(M+2)(27-M)\:=\:210}$

$\implies\:\sf{-M^2+27M-2M+54\:=\:210}$

$\implies\:\sf{M^2-25M+156\:=\:0}$

Now, solve it By splitting the middle term

⇒ M² - 25M + 156 = 0

⇒ M² - 12M - 13M + 156 = 0

⇒ M(M - 12) - 13(M - 12) = 0

⇒ (M - 12)(M - 13) = 0

On comparing we get,

⇒ M = 12, 13

Therefore,

Shefali's marks in Maths = M = 12 and 13

Shefali's marks in English = 30 - M = 18 and 17

Answer 2

Answer:

Solution:-

Let marks of Shefali in Maths be M & Marks in English be E.

There are 2 cases given.

1st case:-

⇒ M + E = 30

⇒ M = 30 - E..............(eq.1)

$\rule{100}{2}$

2nd case:-

⇒ (M + 2) × (E - 3) = 210

⇒ (30 - E + 2) × (E - 3) = 210

⇒ (32 - E) × (E - 3) = 210

⇒ 32E - 96 - E² + 3E = 210

⇒ 35E - E² - 96 = 210

⇒ 35E - E² = 210 + 96

⇒ 35E - E² = 306

⇒ -(E² - 35E) = 306

⇒ E² - 35E = -306

⇒ E² - 35E + 306 = 0

⇒ E² - 18E - 17E + 306 = 0

⇒ E(E - 18)- 17(E - 18) = 0

⇒ (E - 17)(E - 18) = 0

⇒ E - 17 = 0 or, E - 18 = 0

⇒ E = 17 or E = 18

$\rule{100}{2}$

• Putting values in (i) :-

1st case:-

⇒ M = 30 - 17

⇒ M = 13 or,

2nd case:-

⇒ M = 30 - 18

⇒ M = 12

$\therefore{\underline{\rm{Marks \: in \: maths = 12 \: or \: 13 }}}$

$\therefore{\underline{\rm{Marks \: in \: English = 17 \: or \: 18 }}}$