In a class test, the sum of Moulika’s marks in Mathematics and Engli

1.	In a class test, the sum of Moulika’s marks in Mathematics and English is 30. If she got 2 marks more in Mathematics and 3 marks less in English, the product of her marks would have been 210. Find her marks in the two subjects.
Answer» Sum of the marks in Mathematics and English = 30 Let Moulika’s marks in Mathematics be x Then her marks in English = 30 – x If she got 2 more marks in Mathematics, then her marks would be x + 2. If she got 3 marks less in English then her marks would be 30 – x – 3 = 27 – x By problem (x + 2) (27 – x) = 210 ⇒ x(27 – x) + 2(27 – x) = 210 ⇒ 27x – x² + 54 – 2x = 210 ⇒ -x² + 25x + 54 = 210 ⇒ x² – 25x – 54 + 210 = 0 ⇒ x² – 25x + 156 = 0 ⇒ x² – 12x – 13x + 156 = 0 ⇒ x(x – 12) – 13(x 12) = 0 ⇒ (x – 12) (x – 13) = 0 ⇒ x – 12 = 0 or x – 13 = 0 ⇒ x = 12 or x = 13 If x = 12, then marks in Mathematics = 12 English = 30 – 12 = 18 If x = 13, then marks in Mathematics = 13 English = 30 – 13 = 17

In a class test, the sum of Moulika’s marks in Mathematics and English is 30. If she got 2 marks more in Mathematics and 3 marks less in English, the product of her marks would have been 210. Find her marks in the two subjects.

Answer»

Sum of the marks in Mathematics and English = 30

Let Moulika’s marks in Mathematics be x Then her marks in English = 30 – x

If she got 2 more marks in Mathematics, then her marks would be x + 2.

If she got 3 marks less in English then her marks would be 30 – x – 3 = 27 – x

By problem (x + 2) (27 – x) = 210

⇒ x(27 – x) + 2(27 – x) = 210

⇒ 27x – x² + 54 – 2x = 210

⇒ -x² + 25x + 54 = 210

⇒ x² – 25x – 54 + 210 = 0

⇒ x² – 25x + 156 = 0

⇒ x² – 12x – 13x + 156 = 0

⇒ x(x – 12) – 13(x 12) = 0

⇒ (x – 12) (x – 13) = 0

⇒ x – 12 = 0 or x – 13 = 0

⇒ x = 12 or x = 13

If x = 12, then marks in Mathematics = 12

English = 30 – 12 = 18

If x = 13, then marks in Mathematics = 13

English = 30 – 13 = 17