Quantitative Aptitude - Arithmetic Ability Questions

Since it is an isosceles trapezium

So angle C = angle D = x

let A = 180 –D = 180 –x (since AB is parallel to CD)

B = 180-x

A+C = 180 –x + x = 180 degrees (Property of cyclic quadrilateral)

ABCD is cyclic parallelogram with AB // CD and AD // BC

Considering angles A = C = y (Property of parallelogram) and B=D = x Also since it is cyclic A+C = B+D = 180 degrees

So x=y=90 degrees And also opposite sides are equal being a parallelogram

Thus ABCD is a rectangle

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
To be coincident, it must gain 15 min. spaces.55 min. are gained in 60 min.
15 min. are gained in
= (60/55 x 15)min
=16+4/11
The hands are coincident at 16 + 4/11 min past 3