Rajesh can check the quality of 1000 items in 5 hours and Rakesh can complete 75% of the same job in 3 hours. How much time is required for both of them to check 1300 items, if Rakesh stops checking after 2 hours ? 

Given, Rajesh can check the quality of 1000 items in 5 hours

$$\Rightarrow$$ Efficiency of Rajesh = 200 items/hr.

Also given, Rakesh can complete the 75% of same job in 3 hours

$$\Rightarrow$$ time taken by Rakesh to complete 100% of the job = $$\frac{100}{75}\times 3$$ = 4 hours.

$$\Rightarrow$$ Efficiency of Rakesh = 250 items/hr.

Given in the process of checking 1300 items, Rakesh spends only 2 hours. Let say time spent by Rajesh be 't' hours, which is also the total time taken.

Total Work = Efficiency $$\times$$ time taken 

$$\Rightarrow 1300 = 250\times 2 + 200\times t$$

$$\Rightarrow 200t = 800$$

$$\Rightarrow t = 4$$

Hence the time taken in the process of checking 1300 items is 4 hours.