# CAT Practice : Averages, Ratios, Mixtures

Finding the LCM of 6 and 8 will help!

## Minimum number of fruits

Q.23: A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8. What is the minimum number of fruits in his shop?
1. 240
2. 360
3. 120
4. 90

Choice C. 120

## Detailed Solution

Let the number of fruits be 2k, 5k and 8k
Given, 5k – 2k = multiple of 6 and 8
LCM of 6 and 8 is 24
Let’s say 5k – 2k = 24n
3k = 24n
For k to be a natural number and have minimum value, n should be equal to 1
3k = 24
Or k = 8
Hence, the number of fruits = 2k + 5k + 8k
= 15 * 8= 120

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