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The populations of two villages are 1525 and 2600 respectively. If the ratio of male to female population in the first village is 27 : 34 and the ratio of male to female population in the second village is 6 : 7, then what is the ratio of male to female population of these two villages taken together?

The populations of two villages are 1525 and 2600 respectively. If the ratio of male to female population in the first village is 27 : 34 and the ratio of male to female population in the second village is 6 : 7, then what is the ratio of male to female population of these two villages taken together? Correct Answer <span class="math-tex">\(\frac{5}{6}\)</span>

Given:

The populations of two villages are 1525 and 2600 respectively

The ratio of male to female population in the first village is 27 : 34

The ratio of male to female population in the second village is 6 : 7

Concept Used:

If the ratio of male and female is a : b

Then male = a/(a + b)

Calculation:

Population of 1st village = 1525

Ratio of male to female population in the first village is 27 : 34

So,

Number of males in first village = 1525 × (27/61) = 25 × 27 = 675

Number of females in first village = 1525 – 675 = 850

And

Population of 2nd village = 2600

Ratio of male to female population in the 2nd village is 6 : 7

So,

Number of males in 2nd village = 2600 × 6/13 = 200 × 6 = 1200

Number of females in 2nd village = 2600 – 1200 = 1400

Hence,

Ratio of male to female population of these two villages taken together

= (675 + 1200) : (850 + 1400)

= 1875 : 2250

= 5 : 6

∴ The ratio of male to female population of these two villages 5 : 6 taken together

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