Question

Sangeeta and Swati bought two wristwatches from Jamshedpur Electronics at 11:40 AM IST. After buying them, they found that when 60 minutes pass on a correct clock (IST), Sangeeta's wristwatch registers 62 minutes, while Swati's wristwatch registers 56 minutes. Later that day, Sangeeta's wristwatch reads 10:00 PM. What time does Swati's wristwatch show at that moment?

• A. 8:40 PM
• B. 9:00 PM
• C. 9:20 PM
• D. 9:40 PM

Hint:

First find the true elapsed time from how fast Sangeeta's watch runs, then use that true time to find what Swati's slower watch reads.

Answer 1

The Correct Option is B

Step 1: Set up the two watches' rates.
Both watches were correct at 11:40 AM, the moment of purchase. From that point, Sangeeta's watch gains time: for every 60 real minutes, it runs 62 minutes. Swati's watch loses time: for every 60 real minutes, it runs only 56 minutes.

Step 2: Find the real time elapsed when Sangeeta's watch shows 10:00 PM.
From 11:40 AM to 10:00 PM is 10 hours 20 minutes on Sangeeta's watch, which is \(10 \times 60 + 20 = 620\) watch-minutes.
Since 62 watch-minutes correspond to 60 real minutes, the real minutes elapsed are:
\[ 620 \times \frac{60}{62} = \frac{37200}{62} = 600 \text{ minutes} \]
600 minutes is exactly 10 hours.

Step 3: Find the real clock time.
10 hours after 11:40 AM is 9:40 PM. This is the correct, real IST time at the moment Sangeeta's watch shows 10:00 PM.

Step 4: Find what Swati's watch reads at this real time.
Swati's watch runs 56 minutes for every 60 real minutes. Over the real 600 minutes (10 hours) found in Step 2, Swati's watch advances:
\[ 600 \times \frac{56}{60} = 560 \text{ minutes} = 9 \text{ hours } 20 \text{ minutes} \]
Starting from 11:40 AM and adding 9 hours 20 minutes gives 9:00 PM.

Step 5: Rule out the other options.
8:40 PM and 9:20 PM would come from mixing up which watch runs fast and which runs slow, or from applying the wrong ratio to the wrong watch. 9:40 PM is actually the real clock time found in Step 3, not Swati's watch reading, a natural but incorrect mix-up.

Final Answer:
\[ \boxed{\text{9:00 PM}} \]