Question
A company produces three types of products: A, B, and C.
The total number of products produced in a month is 18,000. The production distribution is as follows: 40% of the total products are of type A. The number of products of type B is 25% more than the number of products of type A. The remaining products are of type C. In the next month, the production of type A increases by 20%, the production of type B decreases by 10%, and the production of type C remains the same. What is the percentage increase in the total production from the current month to the next month?Solution
Find the number of products of each type in the current month. Total production = 18,000 products. Type A production = 40% of 18,000 = 0.40 × 18,000 = 7,200 products. Type B production = 25% more than type A = 7,200 + 0.25 × 7,200 = 7,200 + 1,800 = 9,000 products. Type C production = Remaining products = 18,000 - (7,200 + 9,000) = 18,000 - 16,200 = 1,800 products. Now Find the production of each type in the next month. Type A production increases by 20%, so the new production of type A = 7,200 + 0.20 × 7,200 = 7,200 + 1,440 = 8,640 products. Type B production decreases by 10%, so the new production of type B = 9,000 - 0.10 × 9,000 = 9,000 - 900 = 8,100 products. Type C production remains the same, so the production of type C = 1,800 products. Find the total production in the next month. Total production in the next month = 8,640 + 8,100 + 1,800 = 18,540 products. Step 4: Find the percentage increase in total production. Percentage increase = [(Total production in next month - Total production in current month) / Total production in current month] × 100 Percentage increase = [(18,540 - 18,000) / 18,000] × 100 Percentage increase = (540 / 18,000) × 100 = 3%. Correct Option: c
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