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Question

Two different machines are used to manufacture a product. The 1st machine makes the top part, 14 in each batch, and the 2nd machine makes the bottom part, 16 in each batch. Each top part is assembled with the bottom part and released to the sales department.

Find the minimum number of batches needs to be produced by the 2nd machine such that no unassembled parts are left.

A
6
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B
7
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C
8
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D
9
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Solution

The correct option is B 7
The 1st machine produces 14 top parts in a batch.
The 2nd machine produces 16 bottom parts in a batch.

It is given that no unassembled parts are left.
For minimum number of batches from 2nd machine, the total number of assembled products should be minimum.
Number of assembled products is a common multiple of 14 and 16.
The minimum number of assembled products is the least common multiple of 14 and 16.

Using ladder diagram,
LCM =24×7=112

The minimum number of assembled products is 112.

Minimum number of batches required from 2nd machine
=Number of assembled productsNumber of parts per batch
=11216
=7

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