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

Question

A chemical factory produces two kinds of unnatural amino acids: acid A and acid B. Of the acids produced by the factory last year, 1/3 were acid A and the rest were acid B. If it takes 2/5 as many hours to produce acid B per unit as it does to produce acid A per unit, then the number of hours it took to produce the acid B last year was what fraction of the total number of hours it took to produce all the acids?

A. 2/5
B. 4/9
C. 17/35
D. 1/2
E. 5/9

Show Answer

Official Answer

B

A. 2/5
B. 4/9
C. 17/35
D. 1/2
E. 5/9

Hunter2021 · Answer

The question basically asks for the production time of acid A and acid B. From there you will then be able to calculate the relation of the production times to each other. 
Calculate the amount of time they use to produce acid A:
1/3 * 5/5= 5/15
Calculate the amount of time they use to produce acid B:
2/3 * 2/5= 4/15
Add production time for acid A to production time for acid B:
5/15 + 4/15= 9/15
Calculate the ratio of production time of acid B to the total production time:
4/15 / 9/15= 4/15*15/9 = 4/9

RajatGMAT777 · Answer

Bunuel IanStewart KarishmaB
Can You post the solution for this problem, I am not able to understand the logic behind time calculation given the proportion of Amino Acids been manufactured?
Thanks in Advance Experts

IanStewart · Answer

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.

carcass · Answer

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.

Archit3110 · Answer

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

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

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