Question

A student scored a total of 32 marks in class tests in Mathematics and Science. Had he scored 2 marks less in Science and 4 marks more in Mathematics, the product of his marks would have been 253. Find his marks in the two subjects.

Answer 1

Given: Let Mathematics = M and Science = S. We are told: M + S = 32 and (M + 4)(S – 2) = 253.

Step-wise calculation:

1. From M + S = 32, we have S = 32 – M.

2. Substitute into the product equation:

(M + 4)(S – 2) = (M + 4)(32 – M – 2)

= (M + 4)(30 – M)

= 253

3. Expand: (M + 4)(30 – M) = –M² + 26M + 120

So –M² + 26M + 120 = 253.

4. Rearrange: –M² + 26M + 120 – 253 = 0

⇒ –M² + 26M – 133 = 0

Multiply by –1: M² – 26M + 133 = 0

5. Solve quadratic:

Discriminant D = 26² – 4 × 133 

= 676 – 532

= 144, `sqrt(D) = 12`

So `M = (26 ± 12)/2`

⇒ M = 19 or M = 7

6. Find S for each:

If M = 19, S = 32 – 19 = 13.

Check: (19 + 4)(13 – 2)

= 23 × 11

= 253

If M = 7, S = 32 – 7 = 25.

Check: (7 + 4)(25 – 2)

= 11 × 23

= 253

The student’s marks are either Mathematics = 19 and Science = 13 or Mathematics = 7 and Science = 25.