The mean temperature of Monday to Wednesday was 37°C and of Tuesday to Thursday was 34°C. If the temperature on Thursday was $\frac{4}{5}$ that of Monday, the temperature on Thursday was

### Concept & Logic When dealing with overlapping sequence averages (like Mon-Wed and Tue-Thu), the days in the middle cancel out when you find the difference between their sums. This leaves a direct relationship between the first item of the first sequence and the last item of the second sequence. $$\text{Difference in Sums} = \text{First Item} - \text{Last Item}$$ ### Step-by-Step Solution * **Given:** * Mean of Mon, Tue, Wed = 37°C * Mean of Tue, Wed, Thu = 34°C * Thursday ($Th$) = $\frac{4}{5} \times$ Monday ($M$) * **Calculation:** 1. Find the total temperature from Monday to Wednesday: $$M + T + W = 3 \times 37 = 111$$ 2. Find the total temperature from Tuesday to Thursday: $$T + W + Th = 3 \times 34 = 102$$ 3. Subtract the second equation from the first to eliminate the overlapping days ($T$ and $W$): $$(M + T + W) - (T + W + Th) = 111 - 102$$ $$M - Th = 9$$ 4. Substitute the given ratio ($Th = \frac{4}{5}M$, which means $M = \frac{5}{4}Th$) into the equation: $$\frac{5}{4}Th - Th = 9$$ $$\frac{1}{4}Th = 9$$ 5. Solve for Thursday's temperature: $$Th = 9 \times 4 = 36$$ ### Exam Strategy & Shortcut **Direct Difference Multiplier:** You don't need to calculate $111$ and $102$. Just look at the difference in the averages (37°C - 34°C = 3°C). Since there are 3 days in each group, the total difference between the unshared days (Monday and Thursday) is $3 \times 3 = 9$°C. Since $Th = \frac{4}{5}M$, the ratio of $M : Th$ is $5 : 4$. The difference in ratio units is $5 - 4 = 1$ unit. $1$ unit = $9$°C. Thursday is $4$ units. So, $4 \times 9 = 36$°C. Solved in 10 seconds! ### Common Pitfall Calculating the value for Monday ($5 \times 9 = 45$°C) instead of Thursday, and then either panicking because 45 isn't in the options or blindly guessing. Always double-check which specific variable the question is asking for at the very end. ### Final Answer **Therefore, the correct answer is 36°C.**