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# [Smart Math] Ratio Proportion Problem 57

Here’s and example of a SMART MATH problem for RATIO PROPORTION.

### Problem

An officer divided his 35 hour work week as follows:

$\frac{1}{5}$ of his time was spent in sending mails

$\frac{1}{2}$ of his time in filing letters

$\frac{1}{7}$ of his time in reception work

The rest of his time is spent in messenger work.

What is the percent time spent on messenger work?

1. 6%
2. 10%
3. 12%
4. 16%
5. 21%

### The Usual Method

Total time spent in sorting mail, filing letters and reception work = $\left( \frac{1}{5}+\frac{1}{2}+\frac{1}{7} \right)\times 35$hours.

$=\left( \frac{14+35+10}{70} \right)\times 35$

$=\frac{59}{70}\times 35=\frac{59}{2}=$ 29.5 hours.

Hence time spent for messenger work = 35 – 29.5 = 5.5 hours.

Hence % time spent on messenger work = $\frac{5.5}{35}\times 100$

= $\frac{1.1}{7}\times 100$

= $\frac{110}{7}\approx 16$%

(Ans: 4)

Estimated Time to arrive at the answer = 60 seconds.

### Using Technique

We already know that $\frac{1}{5}=20$%, $\frac{1}{2}=50$% and $\frac{1}{7}=14$%.