Quantitative Aptitude - Arithmetic Ability Questions

As minute hand covers, 60 degrees

Minute hand covers 4800/60 = 80°

Required number of students = H.C.F  of 1001 and 910  = 91

The minute hand angle is the easiest since an hour (i.e. 60 minutes) corresponds to the entire 360 degrees, each minute must correspond to 6 degrees. So just multiply the number of minutes in the time by 6 to get the number of degrees for the minute hand.
Here 15 minutes corresponds to 15 x 6 = 90 degrees

Next, you have to figure out the angle of the hour hand. Since there are 12 hours in the entire 360 degrees, each hour corresponds to 30 degrees. But unless the time is EXACTLY something o'clock, you have to write the time as a fractional number of hours rather than as hours and minutes.
Here the time is 9:15 which is (9 + 15/60) = 37/4 hours. Since each hour corresponds to 30 degrees, we multiply 30 to get (37/4)(30) = 277.5 degrees.

Since the hour hand is at 277.5 degrees and the minute hand is at 90 degrees, we can subtract to get the angle of separation. 277.5 - 90 = 187.5 =~ 360 - 187.5 = 172.5 degrees.

$$\begin{gathered} 3 \\ 32 + 3 = 12 \\ 5 \\ 52 + 5 = 30 \end{gathered}$$

Let father's age be 3x and son's age be x years

Father's age after 5 years = 3x + 5 = 26 years

Son's age after 5 years = x + 5 = 12 years

 Ratio of father's and son's ages = 26 : 12 = 13 : 6

Volume of the metal used in the box = External Volume - Internal Volume 

                                                    = [(50 x 40 x 23) - (44 x 34 x 20)] cu.cm  

                                                    = 16080 cu.cm 

Weight of the metal =[(16080 x 0.5)/1000] kg = 8.04 kg.

Angle traced by the hour hand in 6 hours =360o12×6 = 180o.

Let the third number be 100.

Then, the first number = 100 - 20 = 80 and second number = 100 - 30 = 70.

Difference between the first and second number = 80-70 = 10

 Required percentage = 1080 x 100% = 100/8 = 12.5%