# CAT Practice : Percents, Profits

Overall Change

## Overall Change

Q.22: Tensile strength of a material A is a multiple of amount of materials a, b, c, d used. If the amount of material of a, b, c, d are changed by +30%, -30%, -25%, +25% respectively, what will be the overall change in tensile strength of A?
1. No Change
2. +14.68%
3. –14.68%
4. Depends on the initial amount of a, b, c, d

Choice C. –14.68%

## Detailed Solution

Since, tensile strength of A = a x b x c x d, If we assume initial tensile strength to be 100, we can apply successive % changes to arrive at the final figure

100 -30% ---> 70 (Any of the change can be carried out first, the result would be same)

70 + 30% ---> 91

91 + 25% ---> 113.75

113.75 – 25% --> ~85.31

Therefore, percent change in tensile strength = -14.68%

Note – This question could have been solved by just looking at the options. As the individual percentage increase and percentage decrease are same, it will effectively result in an overall percentage decrease for sure because any increase by any % will result in a greater subsequent decrease if same % decrease is applied. Similarly, aby % decrease by any % will result in a smaller subsequent increase if same % increase is applied.

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