Emily sits on a chair in a room. Behind her is a clock. In front of her is a mirror. In the mirror, she sees the image of the clock as shown. The actual time is closest to
(A) 4:10
(D) 6:50
(B) 7:10
(E) 4:50
(C) 5:10

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-103.jpg?height=219&width=225&top_left_y=861&top_left_x=1443)
Emily sits on a chair in a room. Behind her is a clock. In front of her is a mirror. In the mirror, she sees the image of the clock as shown. The actual time is closest to
(A) 4:10
(B) 7:10
(C) 5:10
(D) 6:50
(E) 4:50

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-467.jpg?height=295&width=295&top_left_y=1582&top_left_x=1403)

## Solution

Draw a mirror line to run from 12 o'clock to 6 o' clock and then reflect both the minute and hour hand in this mirror line. The minute hand $(m)$ is reflected to 10 o'clock (which is labelled $m^{\prime}$ ) and the hour hand ( $h$ ) is reflected to just before 5 o'clock $(h$ ').

The required time is 4:50.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-467.jpg?height=377&width=293&top_left_y=1947&top_left_x=1401)

ANSWER: (E)