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

A faster route: skip the real clock altogether and directly compare the two watches' speeds against each other.

Sangeeta's watch runs at $62$ units while $60$ real minutes pass, and Swati's watch runs at $56$ units over the same $60$ real minutes. So the ratio of Sangeeta's watch-minutes to Swati's watch-minutes, for the same stretch of real time, is:

\[ \frac{62}{56} = \frac{31}{28} \]

This means whenever Sangeeta's watch advances by $31$ units, Swati's watch advances by exactly $28$ units, since both are being measured over the identical real time span.

From 11:40 AM to 10:00 PM, Sangeeta's watch has moved forward by $620$ minutes (10 hours 20 minutes). Scale this down by the $28/31$ ratio to get how far Swati's watch has moved:

\[ 620 \times \frac{28}{31} = 20 \times 28 = 560 \text{ minutes} \]

Here $620/31=20$ exactly, which is why the ratio was written as $31:28$ rather than left as $62:56$, since it divides out cleanly.

560 minutes is 9 hours 20 minutes. Adding that to the starting time of 11:40 AM gives 11:40 AM + 9 hours 20 minutes = 9:00 PM.

So Swati's watch shows 9:00 PM at that moment, confirming option B.