Hi Nitesh, 
For clocks and angles, you should solve the questions using the speed of hands of the clocks. 
The hour hand completes the round i.e; 360 degrees in 12 hours or 720 minutes so the speed of the hour hand is 0.5 degrees per minute. The minute hand complete 360 degrees in 60 minutes, so the speed of minute hand is 6 degrees/ minute. 

Now at 8:00, the minute hand is making an angle of 0 degrees with the 12 's clock, and the major angle(counted clockwise) between the 12'o clock mark and the hour hand is 240 degrees. 
Now, in 48 minutes, 
the hour hand will move a total of $$0.5\times\ 48=24^{\circ\ }$$ and the minute hand will move $$6\times\ 48\ =\ 288^{\circ\ }$$. 
Since, the hour hand was already 240 degrees ahead from our previous calculations, the actual angle between these two hands at 8:48 would be; $$240+24-288\ =\ -24^{\circ\ }$$, which means that now the minute hand is 24 degrees ahead of the hour hand. 

We want to increase this difference by 50% of simply by 12 degrees. 
Let the time needed for this to happen be x minutes. 
$$6x-0.5x=12^{ }$$ {angle covered by the minute hand - angle covered by the hour hand}
Giving us $$x\ =\ \frac{12}{5.5}=\frac{24}{11}$$

Hope this would have helped you understand better. 
In such questions, it really helps to draw out a rough sketch of the position of the hands while solving the question. 
Please feel free to reach out for any further questions.

Hi Shubham,

We are given that the time is 8:48. We can find the angle then.

We can put it in the formula = $$\frac{11}{2}M-30H\ =\ \frac{11}{2}\times\ 48-30\times\ 8\ =24$$
So, the hour and minute hand makes an angle of $$24^{\circ\ }$$.
We need to find the minimum time after  8:48 when the angle will increase by 50%.

Currently, it is 24. After the increase, it will be 1.5*24 = 36.
So, the angle will be 36.
We can assume that the angle will be made before 9 only. Hence, the hour will be 8 only.

We know the angle is 36 and the hour is 8. So, we need to find the minutes. We can find by putting the details again into the formula.

$$36=\frac{11}{2}M-30H\ $$
$$36=\frac{11}{2}M-30\times\ 8\ $$
$$36+240=\frac{11}{2}M$$
$$276=\frac{11}{2}M$$
$$276\times\ \frac{2}{11}=M$$
$$\frac{24}{11}=M$$
I hope this clarifies your doubts. Let us know if you face any issues.