Ashifur August 8, 2023 - 20:04
Problem:  A manufacturing company uses two machines A and B with different production 1 capacities. When working alone, machine A can-produce a production lot in 5 hours and machine B can produce the same lot in x hours. When the two machines operate simultaneously to produce the same production lot, it takes them 2 hours to complete the job. How many hours will the machine B take to produce the production lot alone?

View all: JANATA BANK OFFICER (IT) | WRITTEN QUESTION (MATH) SOLVE | 2016

Correct Answer: B alone can do the work in 3$\frac{1}{3}$ hours.

Explanation:

Machine A takes 5 hours to produce = 1 lot

Machine A takes 1 hour to produce = $\frac{1}{5}$ lot

And machine B takes . x hours to produce = 1 lot

Machine B takes 1 hour to produce = $\frac{1}{x}$ lot

Together they take 1 hour to produce = $\frac{1}{5}$+ $\frac{1}{x}$ $\frac{x-5}{5x}$ Portion of lot

Again, they take 2 hours to complete 1 job

They take 1 hour to complete $\frac{1}{2}$ job

We can write, $\frac{x+5}{5x}$ = $\frac{1}{2}$

=> 5x=2x+10

=> 3x = 10

=> x = $\frac{10}{3}$

x = 3$\frac{1}{3}$

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