One third of Rekha’s marks in Hindi exceeds one half of her marks in Science…
2025
One third of Rekha’s marks in Hindi exceeds one half of her marks in Science by 20. If she got 100 marks in the two subjects together, how many marks did she get in Science?
- A.
20
- B.
24
- C.
16
- D.
18
Attempted by 5 students.
Show answer & explanation
Correct answer: C
Concept: A word problem with two related unknowns translates into a pair of linear equations — one equation for each stated relationship between the unknowns. Solving the two equations together (by substitution or elimination) gives the value of each unknown.
Application: Let Hindi marks = H and Science marks = S.
Total marks: H + S = 100, so H = 100 − S.
One third of Hindi marks exceeds one half of Science marks by 20: (1/3)H − (1/2)S = 20.
Substitute H = 100 − S into the second equation: (1/3)(100 − S) − (1/2)S = 20.
Multiply every term by 6 (the LCM of 3 and 2) to clear the fractions: 2(100 − S) − 3S = 120.
Expand and simplify: 200 − 2S − 3S = 120, so 200 − 5S = 120, so 5S = 80, so S = 16.
Cross-check: With S = 16, H = 100 − 16 = 84. One third of 84 is 28, and one half of 16 is 8; 28 − 8 = 20, which matches the condition given in the question.
So Rekha scored 16 marks in Science.