Answer: Option A
:
Each part: 2 Marks
(a) Original speed of Ram $=8$m/s
After training, his speed has increased to = $8+\frac{1}{2}\times 8=12$m/s
Time taken to complete the 100m race $=\frac{100}{12}=\frac{25}{3}$ seconds.
(b) One of the methods is taking the average of the two rational numbers. Let's do it with LCM method here.
Taking LCM of 7 and 8 = 56
$\Rightarrow \frac{5}{7}=\frac{5\times 8}{7\times 8}=\frac{40}{56}$
$\Rightarrow \frac{7}{8}=\frac{7\times 7}{8\times 7}=\frac{49}{56}$
$\therefore$ Four rational numbers between $\frac{40}{56}$   and  $\frac{49}{56}$ can be $\frac{43}{56},\frac{44}{56},\frac{45}{56},\frac{46}{56}$
In standard form the rational numbers are $\frac{43}{56},\frac{11}{14},\frac{45}{56},\frac{23}{28}$