Question 121542
Mathematically, we can calculate  the hand angles in terms of time expressed in {{{hours}}} and {{{minutes}}}:
 {{{(h:m)}}}.  
Since the {{{minute}}}{{{ hand}}} moves {{{360 }}}degrees in {{{60}}} minutes, it moves {{{6}}} degrees {{{per}}}{{{ minute}}}, and {{{angle}}} of minute hand{{{ (A[m]) =6m}}}.  
The {{{hour}}}{{{ hand}}} make a complete revolution in {{{12}}} hours ({{{720}}} minutes).  So the hour hand moves {{{1/12}}} of a revolution({{{30}}} degrees) for each hour plus {{{1/720}}} of a revolution ({{{1/2 }}}degree) for each minute.  . 
 So the angle of hour hand is: {{{(A[h])=30h + m / 2}}}.  
If we set   {{{A[m] = A[h] + 90}}} to calculate {{{when}}} the minutes hand is {{{90}}} degrees ahead, we get:
{{{ 6m = 30h + m/2 +90}}}
Solving for {{{m}}}, we get {{{m = (60h+180) / 11}}}.  
At {{{12}}} o'clock (call it {{{0}}}) we have to wait {{{16.36}}} minutes before the minute hand gets {{{90}}} degrees ahead. 
 
We get {{{90}}} degrees {{{44}}} times in {{{24}}} hours. 

so, your answer is :

c) {{{highlight(16 4/11_ minutes)}}}