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Machine A takes x hours to produce a batch of bolts. It takes \(\frac{2x}{5}\) hours for machine A and B working simultaneously to produce the same batch of bolts. In terms of \(x\), how many hours would it take machine B to produce the same batch of bolts working at its individual rate?
A) \(\frac{ x}{5}\)
B) \(\frac{x}{4}\)
C) \(\frac{2x}{3}\)
D) \(\frac{3x}{5}\)
E) \(\frac{x}{2}\)
A) \(\frac{ x}{5}\)
B) \(\frac{x}{4}\)
C) \(\frac{2x}{3}\)
D) \(\frac{3x}{5}\)
E) \(\frac{x}{2}\)
22 Apr 2025, 00:51
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Bunuel
Let, x = 5
A takes 5 hours
A+B take 2 hours
i.e. A's 1 hour work = 1/5
i.e. (A+B)'s 1 hour work = 1/2
i.e. B's 1 hour work = (1/2)-(1/5) =3/10
i.e. B's time = 10/3 hours
A) \(\frac{ x}{5}\) for x= 5, it's 5/5=1 NO
B) \(\frac{x}{4}\) for x= 5, it's 5/4 NO
C) \(\frac{2x}{3}\) for x= 5, it's 10/3 YES
D) \(\frac{3x}{5}\) for x= 5, it's 3*5/5=3 NO
E) \(\frac{x}{2}\) for x= 5, it's 5/2 NO
Answer: Option C
Related Video:
Archit3110
22 Apr 2025, 01:08
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Rate of A 1/x
Rate of B be 1/Y
Combined rate 5/2x
1/x+1/y =5/2x
1/y = 5/2x - 1/x
1/y = 5x-2x / 2x^2
1/y= 3x/2x^2
1/y= 3/2x
Y =2x/3 hours
Option C
Rate of B be 1/Y
Combined rate 5/2x
1/x+1/y =5/2x
1/y = 5/2x - 1/x
1/y = 5x-2x / 2x^2
1/y= 3x/2x^2
1/y= 3/2x
Y =2x/3 hours
Option C
Bunuel
