There are 2 clocks A and B. The angle between minutes and hour hand of the clock A is x degrees and that between hands of clock B is y degrees. The sum of x and y is 180 degrees and difference between x and y is 40 degrees. If time on clock A is between 2 and 3 and on clock B is between 4 and 5, which of these is correct time combination of both clocks?

Option 1 : (30 + 10/11) minutes past 2 and (34 + 6/11) minutes past 4

According to question,

x + y = 180

x – y = 40

Solving both the equations, x = 110 and y = 70

Clock A

Angle between the hands = 11 × m/2 – 30 H

m denotes the minute hand and H denotes the hour hand

Angle = 110 degrees               H = 2

110 = 11 × m/2 – 30 × 2

m = 340/11 = (30 + 10/11)

Time on Clock A is (30 + 10/11) minutes past 2.

Clock B

Angle between the hands = 11 × m/2 – 30 H

m denotes the minute hand and H denotes the hour hand

Angle = 70 degrees                 H = 4

70 = 11 × m/2 – 30 × 4

m = 380/11 = (34 + 6/11)