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3 bars of length 16, 20 and 24 cm are cut into equal parts and are packed in a box which can contain maximum of two pieces of such rods. Find the minimum number of boxes required.6012830

Question

3 bars of length 16, 20 and 24 cm are cut into equal parts and are packed in a box which can contain maximum of two pieces of such rods. Find the minimum number of boxes required.6012830

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Solution

Sure, let's solve this step by step:

Step 1: Find the greatest common divisor (GCD) of the lengths of the bars. The GCD of 16, 20, and 24 is 4 cm. This means that each bar will be cut into pieces of 4 cm each.

Step 2: Calculate the number of pieces each bar will be cut into. The 16 cm bar will be cut into 4 pieces, the 20 cm bar into 5 pieces, and the 24 cm bar into 6 pieces.

Step 3: Calculate the total number of pieces. This is 4 + 5 + 6 = 15 pieces.

Step 4: Since each box can contain a maximum of two pieces, divide the total number of pieces by 2. This gives 15 / 2 = 7.5.

Since we can't have half a box, we'll need to round up to the nearest whole number. So, we'll need a minimum of 8 boxes to pack all the pieces.

This problem has been solved

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