1440 men had sufficient food for 32 days in a camp. How many men may leave the camp so that the same food is sufficient for 40 days when the ration is increased by 1.5 times?
Ten men can assemble 400 cycles in 8 days. How many cycles will 5 men assemble if they work for 16 days?
Answer (2)
A total of 672 men can leave the camp for the remaining food to last 40 days with an increased ration. In 16 days, 5 men can assemble 400 cycles. The calculations show efficient resource management and work rates.
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This problem involves two parts: calculating the number of men who may leave the camp while maintaining sufficient food for 40 days, and determining how many cycles 5 men can assemble in 16 days.
Part 1: Food Supply and Men in a Camp
We start by understanding the initial setup: 1440 men have enough food to last for 32 days. We want to determine how many men can leave so that the food lasts for 40 days with an increased ration.
Initial Consumption Calculation : The total consumption by 1440 men in 32 days is calculated as: Total food = 1440 × 32
Adjusted Consumption with Increased Ration : With the ration being increased by 1.5 times, the food will last for 40 days. To reflect this change: Increased Consumption per Day = 40 Total food
Calculate New Number of Men : Let x be the number of men that remain: x × 1.5 × 40 = 1440 × 32 Solving for x : x = 1.5 × 40 1440 × 32 After calculation, x = 768 .
Determine Number of Men Who May Leave : 1440 − 768 = 672 . Therefore, 672 men may leave the camp.
Part 2: Cycle Assembly Problem
Original Assembly Rate : 10 men can assemble 400 cycles in 8 days. Therefore, the rate of cycles per person per day is: Rate per man per day = 10 × 8 400 = 5
Calculate Cycles for 5 Men Over 16 Days : With 5 men working 16 days and maintaining this rate: Total cycles = 5 × 5 × 16 = 400
Thus, 5 men can assemble 400 cycles in 16 days.
