Question

Q24. Machines A and B always operate independently and at their respective constant rates. When working alone, machine A can fill a production lot in 5 hours, and machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x ?

• A. ( a) $3\frac{1}{3}$
• B. (b) 3
• C. (c) $2\frac{1}{2}$
• D. (d) $2\frac{1}{3}$

Answer 1

The correct option is A

( a) $3\frac{1}{3}$

Machine A efficiency = 1/5 per hour;

Machine B efficiency = 1/x per hour;

When working together, efficiency = (1/5 + 1/x);

Given, (1/5+1/x)*2 = 1;

5x=10 + 2x; x=10/3