Quant Boosters  Maneesh  Set 2

Q26) At what time between 4 and 5 will the hands of a watch coincide?

At 4 o clock the hands are 20 minutes apart.
In order to coincide minute hand must gain 20 minutes.
Minute hand gains 55 minutes in 60 minutes.
Hence it will gain 20 minutes in > 60*20/55 = 240/11 = 21 9/11 minutes
Hence hands will coincide at 21 9/11 minutes past 4.

Q27) At what time between 4 and 5 will the hands of a watch point in opposite directions?

They will be in opposite direction when there is 30 minute space between them.
This will happen when minute hand gains 50 minutes (at 4 o clock hands are 20 minutes apart).
Minute hand gains 50 minutes in 60 * 50/55 = 600/11 =54 6/11 minutes.
Hence hands point in opposite directions at 54 6/11 past 4.

Q28) My watch which gains uniformly is 2 minutes slow at noon on Sunday and is 4 minutes 48 seconds fast at 2 p m on the following Sunday. When it was correct?

Sunday noon to next Sunday 2 PM = (24 * 7) + 2 = 170 hours
In 170 hours watch gains 2 + 4 + 48/60 minutes
In 170 hours watch gains 6 4/5 minutes.
Hence in order to gain 2 minute watch will take 170 * 5 * 2/34 = 50 hours
50 hours means 2 days and 2 hours.
That means at 2 PM on Tuesday it was correct.

Q29) From noon by how many degrees has the minute hand moved to 2:40 ?

One hour means minute hand moves 360 degree
2 hours means minute hand moves 720 degree
40 minute means minute hand moves 240 degree
Hence total = 720+240 = 960 degrees.How many degrees does an hour hand move in 20 minutes?
In one hour hour hand moves 30 degrees.
Hence in 20 minutes hour hand moves 30/3 = 10 degrees.

Q30) What is the angle between the minute hand and hour hand of a clock when the time is 7:30?

Angle = 30x  11y/2
= 30 * 7 – 11 * 30/2
= 210 – 165
= 45 degree.