# CAT Practice : Percents, Profits

What percentage of alloy 1 needs to be mixed with Alloy 2 to get alloy 3.

## Percentages - Integers

Q.4: A earns 25% more than B. C earns 25% more than A. A earns 20% more than D. E earns 20% more than A. A, B, C, D, and E earn integer amounts less than Rs. 100. What is the total amount earned by all five of them put together?
1. Rs. 300
2. Rs. 245
3. Rs. 305
4. Rs. 480

Choice C. Rs. 305

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## Detailed Solution

A = ${5 \over 4}$ x B or, B = ${4 \over 5}$ x A
C = ${5 \over 4}$ x A
A = ${6 \over 5}$ x D, or D = ${5 \over 6}$ x A
E = ${6 \over 5}$ x A

In order for the amounts earned by A, B, C, D and E to be integers, the amount earned by A should be a multiple of 4, 5 and 6. Or, the amount earned by A should be a multiple of 60. The only multiple of 60 that is a 2–digit number is 60.

So, if A earns Rs. 60, B should earn Rs. 48. C should earn Rs. 75, D should earn Rs. 50 and E should earn Rs. 72.

The total income earned by all 5 of them should be equal to Rs. 60 + Rs. 48 + Rs. 75 + Rs. 50 + Rs. 72
=> Rs. 305

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