A factory requires 42 machines to produce a given number of toys in 63 days. How many machines are required to produce the same number of toys in 54 days?
Given: 42 machines produce toys in 63 days. Find machines needed for 54 days.
Formula: Machines × Days = Constant (Inverse Proportion)
Calculation: Total work = = 2646 machine-days New machines = 2646 ÷ 54 = 49 machines
Answer: 49 machines are required to produce the same number of toys in 54 days.
Explanation
The chapter explains inverse proportion for production problems. Machines × Days = Constant work. Initial: = 2646 machine-days. New machines = 2646 ÷ 54 = 49 machines.
Solution Steps
Step 1: Calculate total work in machine-days: 42 machines × 63 days = 2646 machine-days
Step 2: Calculate machines needed: 2646 machine-days ÷ 54 days = 49 machines