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08 Jul 2018, 21:37
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:23) correct
32%
(03:01)
wrong
based on 401
sessions
History
Date
Time
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Not Attempted Yet
Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?
(A) 15.75
(B) 18
(C) 18.75
(D) 27.5
(E) 30
(A) 15.75
(B) 18
(C) 18.75
(D) 27.5
(E) 30
09 Jul 2018, 05:57
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Solution
Given:
- • Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes
• Robot A’s rate of polishing is \(\frac{3}{5}\) that of robot B
To find:
- • How many minutes would it take robot A alone to polish 165 pounds of gemstones
Approach and Working:
If robot B polishes x gemstones per minute, then robot A polishes \(\frac{3x}{5}\) gemstones per minute
- • Therefore, in 6 minutes, they can polish \(6 (x + \frac{3x}{5}) = 6 * \frac{8x}{5}\) gemstones
• Or we can write, \(6 * \frac{8x}{5} = 88\)
Or, \(x = 88 * \frac{5}{6} * 8 = \frac{55}{6}\) gemstones/minute
Therefore, in 1 minute, robot A can polish = \(\frac{55}{6} * \frac{3}{5} = \frac{11}{2}\) gemstones = 5.5 gemstones
- • Hence, to polish 165 gemstones, robot A will take \(\frac{165}{5.5} = 30\) minutes
Hence, the correct answer is option E.
Answer: E
08 Jul 2018, 22:18
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Given that \(\frac{1}{A}\) + \(\frac{1}{B}\) = \(\frac{1}{6}\).....(1)
And aslo given that A = \(\frac{3}{5}\)B.......(2)
Now, substituting (2) in (1) and simplifying, we get B =16min and A = 9.6min (This is the time taken by individual robots to polish 88 pounds)
Now for 165 pounds. The time taken by A is \(\frac{165*9.6}{88}\) = 18min.
Ans is B
Please give kudos if you liked the solution
And aslo given that A = \(\frac{3}{5}\)B.......(2)
Now, substituting (2) in (1) and simplifying, we get B =16min and A = 9.6min (This is the time taken by individual robots to polish 88 pounds)
Now for 165 pounds. The time taken by A is \(\frac{165*9.6}{88}\) = 18min.
Ans is B
Please give kudos if you liked the solution
