Smita works in her office for 6 hours and Kajal works in her office for 7 hours 30 minutes. Find the ratio of their working hours. [ESIC—UDC Exam, 2016]

### Concept & Ratio Calculation To find the ratio between two quantities, they must be expressed in the same unit. $$ \text{Ratio} = \frac{\text{Value } A}{\text{Value } B} $$ ### Step-by-Step Solution * **Given:** Smita's working time = 6 hours. Kajal's working time = 7 hours 30 minutes. * Convert both times to minutes to ensure consistency. * Smita's time in minutes = $6 \times 60 = 360$ minutes. * Kajal's time in minutes = $(7 \times 60) + 30 = 420 + 30 = 450$ minutes. * Now, find the ratio: $360 : 450$ * Divide both sides by 10: $36 : 45$ * Divide both sides by their greatest common divisor (9): $4 : 5$ ### Exam Strategy & Shortcut Instead of converting to minutes, you can keep them in hours using decimals: 6 hours to 7.5 hours. Multiply both by 2 to remove the decimal, getting 12 to 15. Divide by 3 to get the ratio 4:5. ### Common Pitfall A common mistake is trying to write the ratio directly as $6 : 7.3$, which incorrectly assumes 30 minutes is 0.3 hours rather than 0.5 hours. ### Final Answer Therefore, the correct answer is **4 : 5**.