English: 90% of runners in a marathon successfully completed it. 30% of these runners were men. How many total runners began the marathon if 270 men completed it?

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90% of runners in a marathon successfully completed

cal1805p8uo38

23.01.2022

The total runners who began the marathon is 1000

Explanation:

Given:

Runners who completed the marathon = 90%

Men = 30%

Number of men completed the marathon = 270

Total runners who began the marathon = ?

Let the total runners be x

According to question:

Runners who completed the marathon = $\frac{90}{100} X x$

= 0.9x

and,

$\frac{30}{100} X 0.9 x = 270$

Solving further:

$0.9x = \frac{270 X 100}{30} \\\\x = \frac{270 X 100}{30 X 0.9} \\\\x = 1000$

Therefore, total runners who began the marathon is 1000

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