Question

A student scored a total of 32 marks in a class test in maths and science. had he scored 2 marks less in science and 4 more in maths, the product of his marks would have been 253. find his marks in two subjects

Answer 1

Let the marks in Maths be 'm' & marks in science be 's'

Given,m + s = 32

If he had scored 2 marks less in science, that is, (s-2) and 4 marks more in maths, that is (m+4), then the product equals 253
(s-2)*(m+4) = 253
 Substitute s = 32-m for 's' in above equation
(32-m-2)*(m+4) = 253
(30-m)*(m+4) = 253
30m - m^2 - 4m + 120 = 253
26m - m^2 = 133
m^2 - 26m + 133 = 0
m^2 - 19m - 7m + 133 = 0
m(m-19) - 7(m-19) = 0
(m-7)(m-19) = 0
So m = 19 OR 7
If m = 19, s = 32-19 = 13
If m = 7, s = 32-7 = 25

Both the marks satisfy the given condition
So the marks are either (Maths=19, Science=13) or (Maths=7, Science = 25)

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let marks in Mathematics be x.

And, marks in Science be 32 - x.

According to the Question,

⇒ (32 - x - 2)(x + 4) = 253

⇒ (30 - x)(x + 4) = 253

⇒ 26x - x² + 120 = 253

⇒ x² - 26x + 133 = 0

⇒ x² - 19x - 7x + 133 = 0

⇒ x(x - 19) - 7(x - 19) = 0

⇒ (x - 19) (x - 7) = 0

⇒ x = 19, 7

If x = 19, then,

Marks in Mathematics = x = 19

Marks in Science = 32 - x = 13

If x = 7, then,

Marks in Mathematics = x = 7

Marks in Science = 32 - x = 25