Exams

At 9 o’clock, the hour hand is at 9 and the minutes hand is at 12, i.e., the two hands are 15 min. spaces apart.
So, the minute hand should gain = (30 - 15) minutes = 15 minutes
55 minutes will be gained in 60 min.
15 minutes spaces will be gained in ((60/55) x 15) min. = 180/11 min.
The hands will be in the same straight line but not together i.e.,in 180 degrees at 180/11 min. past 9.

Side of smallest cube = L.C.M of 5, 10, 20 = 20cm  

Volume of the cube = (20 x 20 x 20)cu.cm = 8000 cu.cm  

Volume of the block= (5 x 10 x 20)cu.cm = 1000 cu.cm  

Number of blocks = (8000/1000) = 8

A book has a spine to hold all the pages, but it has no bones.

Let the present ages of Ajay and Vijay be 'A' and 'V' years respectively.

=> A - 8 = 4/3 (V - 8) and A + 8 = 6/5 (V + 8)

=> 3/4(A - 8) = V - 8 and 5/6(A + 8) = V + 8

V = 3/4 (A - 8) + 8 = 5/6 (A + 8) - 8

=> 3/4 A - 6 + 8 = 5/6 A + 20/3 - 8

=> 10 - 20/3 = 10/12 A - 9/12 A

=> 10/3 = A/12 => A = 40.

Let the mother's present age be x years.

Then, the person's present age = 2/5 x years.

(2x/5 + 8) = 1/2 (x + 8)

2(2x + 40) = 5(x + 8) => x = 40.