# CAT Practice : Averages, Ratios, Mixtures

Averages

## Averages

Q.49: Average of ‘n’ number is t. One of the numbers ‘s’ is replaced by ‘z’ and the new average becomes u. What is the relation b/w n, t, s, u and z?
1. $\frac{(u-3)}{(z-s)} = \frac{1}{n}$
2. $\frac{(z-s)}{u} = \frac{1}{n}$
3. $\frac{(t-u)}{(s-z)} = \frac{1}{n}$
4. $\frac{(u-3)}{(z-s)} = \frac{1}{n}$

Choice C. $\frac{(t-u)}{(s-z)} = \frac{1}{n}$

## Detailed Solution

New Average, $u = t + \frac{(z-s)}{n} (when z > s)$………………..(1)
$= t - \frac{(s-z)}{n} (when s < z)$
$= t + \frac{(z-s)}{n}$ (same as (1))
= ) $u – t = \frac{(z-s)}{n}$
= ) $\frac{(u – t)}{(z-s)} = \frac{1}{n}$
= ) $\frac{(t - u)}{(s-z)} = \frac{1}{n}$

Correct Answer: $\frac{(t-u)}{(s-z)} = \frac{1}{n}$

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