A body moving with uniform acceleration covers 100m in the first 10s and 150m in the next  10s. The acceleration of the body (in m/s^-2) is

Let ‘u’ and ‘a’ be the initial velocity and acceleration of the body respectively
$\therefore$ From equation  $S=ut+\frac{1}{2}a{t}^2$
Step-I
$100=10u+\frac{1}{2}a{\left(10\right)}^2$ 
$\Rightarrow 10=u+5a\mathrm{..........}\left(1\right)$ 
Step-II
The total distance covered in the total time of 20S is 100+150=250m 
$\therefore 250=20u+\frac{1}{2}a{\left(20\right)}^2$ 
$\Rightarrow 250=20u+200a$ 
$\Rightarrow 25=2u+20a\mathrm{........}\left(2\right)$ 
On solving equations (1) & (2)
Acceleration  $a=0.5m/s^2$