we are basically asked to find rate of B so w=rt
1) not suff as no rate are given
2) suff, it says rate B= 1.5 rate A, from questn we have 1/a + 1/b = 1/20 , hence we can find time B and eventually time required to build 50 components

A+B are producing 50 components in 20 minutes.

(1) A produced 10 fewer than B, this means A produced 20 components in 20 minutes while B produced 30 components in 20 minutes. So if B produces 30 in 20 minutes, it produces 1.5 components per minute and thus we can find the time required to produce 50 = 50/1.5 minutes. Sufficient.

(2) So if A produces 'x' components per minute, B produces '1.5x' components per minute. So in 1 minute, A+B produce = x+1.5x = 2.5x components. Thus in 20 minutes they produce = 20*2.5x = 50x components.. but this is given as 50 only. So x=1. Thus A produces 1 per minute while B produces 1.5 per minute. This data now becomes same as in first statement. So Sufficient.

Hence D answer

Statement 1:
Machine A produced 20 so Machine B produced 30.
Rate of production of B = 20 / 30 per minute or 20/ 30 minutes to make 1 component => 20/30*50
Therefore to make 50 components = 33.33 minutes
SUFFICIENT

Statment 2:
Let rate of A = x components / minute, therefore rate of B = 1.5x components / minute.
(x + 1.5x) * 20 = 50 = > x = 1 components per minute. = > Rate of B = 1.5 components / per minute
Therefore, to produce 50 components, it will take B approx 33.33 minutes
SUFFICIENT

Ans - D

Ans: D

We are given that Machine A and machine B together produced 50 components in 20 minutes. and we need to find time taken by B for 50 components.

Stat (1): Machine A produced 10 fewer components than did machine B.
lets say MA produces x comp/min so MB produces x+10 Comp/min. Together they will produce 2x+10 comp/min, which is equal to 50/20 (given). here we can get the value of x which will give us the speed of MB. (Suff)

Stat (2): The rate at which machine B works is 50 percent faster than the rate at which machine A works. Again relation between MA and MB speed is given so we can find the individual speed and thus (Suff)

Final Ans: D (Both stat alone are sufficient to ans the question)
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Given : Combined rate = 50 components / 20 minutes

A + B = 50 ----- (I)

Question : Time taken by B to produce 50 components ?

St 1: A = B - 10 -----(II)

From I and II we get

B + B - 10 = 50

2B = 60

B = 30 components / 20 minutes

We can find out time for producing 50 components (Sufficient)

St 2: R(B) = 1.5R(A) -----(III)

From I and III we an again find out production capacity of B. (Sufficient)

(D)
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(1) Machine A produced 10 fewer components than did machine B.

It's not clear, we don't know the period of time in which Machine A produced 10 fewer than Machine B. Event we got some information in the question, on my opinion its not really obvious to conclude the split.

I'm maybe wrong on this point, if someone have an explanation, I'll be happy to read it. Thanks.

Isn't the coloured part a little ambiguous as in what time A produced 10 fewer components is not mentioned in the question.
Thanks in advance.