Machine A can produce 1,000 widgets in 5 hours. Machin

Machine A can produce 1,000 widgets in 5 hours. Machine B can produce 1,000 widgets in 10 hours. If machines A, B, and C working
independently and simultaneously can produce 1,000 widgets in 3 hours, how many hours would it take machine C alone to produce
1,000 widgets?

So, In 3 hours

Machine A produces 600 widgets ( 1000/5 = 200widgets/hour)
Machine B produces 300 widgets ( 1000/10 = 100widgets/hour)
so, Machine c produces 100 widgets in 3 hours, This implies Machine C will produce 1000 widgets in 30 hours.

ANSWER OPTION E

Machine A can produce 1,000 widgets in 5 hours. Machine B can produce 1,000 widgets in 10 hours. If machines A, B, and C working
independently and simultaneously can produce 1,000 widgets in 3 hours, how many hours would it take machine C alone to produce
1,000 widgets?

Machine A can produce 1,000 widgets in 5 hours.
So, In 1 hour, Machine A can produce 200 widgets
In 3 hours, Machine A can produce 600 widgets

Machine B can produce 1,000 widgets in 10 hours.
So, In 1 hour, Machine B can produce 100 widgets
In 3 hours, Machine B can produce 300 widgets

If machines A, B, and C working independently and simultaneously can produce 1,000 widgets in 3 hours

We know that, A produces 600 widgets and B produces 300 widgets, so, C must produce 100 widgets in 3 hours.

Therefore, C will take 30 hours to produce 1,000 widgets.

Choice E is the answer.

Let the time taken by mc C be x.
Hence 1/10+1/5+1/x=1/3
Solve to get x=30

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Let Machine C make 1000 widgets in c hours
Therefore,
\(300+\frac{1000}{c} = \frac{1000}{3}\)
or, c = 30

Answer: E

OA is E i.e., 30 hours.

Lets assume C takes x hours to make 1000 widgets

so rate of C = 1000/x widgets per hour

similarly rate of A = 1000/5 widgets per hour
and rate of B = 1000/10 widgets per hour

as given when A ,B and C work simultaneoulsy they can finish job in 3 hours

so 3*(per hour work of A) + 3*(per hour work of B ) + 3*(per hour work of C) = 1000

putting values from above we will get

3*(1/5) + 3*(1/10) + 3(1/x) =1

solving above eqauation we will get x =30 hours .

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