The mean temperature of Monday to Wednesday was 37°C and of Tuesday to…
2024
The mean temperature of Monday to Wednesday was 37°C and of Tuesday to Thursday was 34°C, if the temperature on Thursday was 4/5th that of Monday, then what was the temperature on Thursday?
- A.
36.5°C
- B.
36°C
- C.
35.5°C
- D.
34°C
Attempted by 9 students.
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Correct answer: B
Concept: For a set of values, mean × count = sum. When two overlapping groups of days share some days but differ in one, subtracting their sum equations cancels the shared days and directly isolates the difference between the two days that are not shared — turning an averages problem into a simple linear equation.
Let Mo, Tu, We, Th denote the temperatures on Monday, Tuesday, Wednesday, and Thursday. From the given means: Mo + Tu + We = 3 × 37 = 111 (Eq. 1) and Tu + We + Th = 3 × 34 = 102 (Eq. 2).
Subtracting Eq. 2 from Eq. 1 cancels Tu and We, the days common to both windows: Mo − Th = 111 − 102 = 9 (Eq. 3).
The given ratio Th = (4/5) × Mo rearranges to Mo = (5/4) × Th.
Substituting Mo = (5/4) × Th into Eq. 3 gives (5/4)Th − Th = 9, i.e. (1/4) × Th = 9.
Solving, Th = 9 × 4 = 36°C.
Cross-check: with Th = 36°C, Mo = (5/4) × 36 = 45°C. Then Tu + We = 111 − 45 = 66°C from Eq. 1, and Tu + We + Th = 66 + 36 = 102°C, which matches Eq. 2 exactly — confirming the result.
Thursday's temperature was 36°C.