In an examination, A obtained three times the marks obtained by B. If the…
2021
In an examination, A obtained three times the marks obtained by B. If the difference between their marks is 12, how many marks did A obtain?
Answer: C. 18 — ConceptWhen one quantity is a fixed multiple of another, represent both quantities with one variable. Their difference then gives a linear equation in that…
- A.
14
- B.
16
- C.
18
- D.
20
Attempted by 5 students.
Show answer & explanation
Correct answer: C
Concept
When one quantity is a fixed multiple of another, represent both quantities with one variable. Their difference then gives a linear equation in that variable.
If A = kB, then A − B = (k − 1)B. Solving for B first makes the larger quantity easy to obtain.
Application
Let B = x marks. Since A obtained three times B’s marks, A = 3x.
Their difference is 12, so A − B = 12.
Substitute A = 3x and B = x: 3x − x = 12.
Combine like terms: 2x = 12, hence x = 6.
Therefore, A = 3x = 3 × 6 = 18 marks.
Cross-check
With A = 18 and B = 6, A is three times B and their difference is 18 − 6 = 12. Both conditions are satisfied.
Result
A obtained 18 marks.