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.
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