A chemical factory produces two kinds of unnatural amino acids: acid A

The question is about ratios alone, so we can freely invent quantities and work with those (to avoid letters and fractions). If 1/3 of the acid was type A, then we can imagine the factory produced 1 unit of acid A, and thus 2 units of acid B. We also know the time it takes to produce one unit of acid B is 2/5 of the time it takes to produce one unit of acid A. So we can imagine it takes 2 hours to produce a unit of acid B, and thus 5 hours to produce a unit of acid A. Since the factory produced 2 units of B, that took 2*2 = 4 hours, and since it produced 1 unit of acid A, that took 1*5 = 5 hours, so 4/(4 + 5) = 4/9 of the time was spent producing acid B.

OE

Let us use plugging in numbers for unknown values.

Let the Total acid produced= 30 units ⇒Acid A=1/3 30=10 units

Acid B= 20 units

Let time taken to produce per unit Acid A= 5 hours ⇒Time taken to produce per unit Acid B= 2/5 ∗ 5=2 hours

Number of hours the factory took to produce acid B=2 × 20= 40

Total Number of hours factory took to produce both acid A and acid B= (2 × 20) + (5 × 10) = 90

Then, 40/90 = 4/9

Hence, the answer is B.

when given data in fractions always take LCM of Dr and take a simple value
in this case
let total Unit of Acid be 15
so A will be 5 and B is 10
also for time for a be 5
so B takes 2 hrs
total time to mfg B acid ; 10*2; 20 hrs
all the acid ; 5* 5 ; 25+20 ( total 45)
20/45 ' 4/9
option B

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