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In three 20-20 cricket match series play in three different stadiums whose capacities ratio 3 ∶ 2 ∶ 1 are packed with male and female audience. The ratio of male and female audience in the stadium are 5 ∶ 2, 4 ∶ 1, and 4 ∶ 1 respectively. On special demand of audience one more match is played and the total audience for the match is sum of 1 / 3 of first match audience, 1 / 2 of second match audience and 1 / 7 of third match audience then find the percent of female in the fourth match.

In three 20-20 cricket match series play in three different stadiums whose capacities ratio 3 ∶ 2 ∶ 1 are packed with male and female audience. The ratio of male and female audience in the stadium are 5 ∶ 2, 4 ∶ 1, and 4 ∶ 1 respectively. On special demand of audience one more match is played and the total audience for the match is sum of 1 / 3 of first match audience, 1 / 2 of second match audience and 1 / 7 of third match audience then find the percent of female in the fourth match. Correct Answer 24%

Given:

Ratio of the capacities of all three stadiums = 3 ∶ 2 ∶ 1

The ratio of male and female audience in the first stadium= 5 ∶ 2

The ratio of male and female audience in the second stadium = 4 ∶ 1

The ratio of male and female audience in the third stadium = 4 ∶ 1

Number of audience has taken from first stadium for 4th match = 1 / 3

Number of audience has taken from second stadium for 4th match = 1 / 2

Number of audience has taken from third stadium for 4th match = 1 / 7

Calculations

Let the capacities of all three stadiums be 3x, 2x and x

For first stadium

⇒ Number of male audience = (3x / 7) × 5 = 15x / 7

⇒ Number of female audience = (3x / 7) × 2 = 6x / 7

For second stadium

⇒ Number of male audience = (2x / 5) × 4 = 8x / 5

⇒ Number of female audience = (2x / 5) × 1 = 2x / 5

For third stadium

⇒ Number of male audience = (x / 5) × 4 = 4x / 5

⇒ Number of female audience = (x / 5) × 1 = x / 5

∵ For forth stadium the total audience for the match = 1 / 3 of first match audience + 1 / 2 of second match audience + 1 / 7 of third match

⇒ 1 / 3 of the first match audience then male audience = (15x / 7) × (1 / 3) = 5x / 7

⇒ 1 / 3 of the first match audience then female audience = (6x / 7) × (1 / 3) = 2x / 7

⇒ 1 / 2 of the second match audience then male audience = (8x / 5) × (1 / 2) = 4x / 5

⇒ 1 / 2 of the second match audience then female audience = (2x / 5) × (1 / 2) = x / 5

⇒ 1 / 7 of the third match audience then male audience = (4x / 5) × (1 / 7) = 4x / 35

⇒ 1 / 7 of the third match audience then female audience = (x / 5) × (1 / 7) = x / 35

Hence the total audience for fourth match = (5x / 7) + (2x / 7) + (4x / 7) + (x / 5) + (4x / 35) + (x / 35)

⇒ 75x / 35

Hence the female audience for fourth match = (2x / 7) + (x / 5) + (x / 35)

⇒ 18x / 35

∴ Percent of female in the fourth match = {(18x / 35) / (75x / 35)} × 100 = 24%

Alternate method

Ratio of the capacities of all three stadiums = 3 ∶ 2 ∶ 1

⇒ 3 × 35 ∶ 2 × 35 ∶ 1 × 35

⇒ 105 ∶ 70 ∶ 35

∴ The audience first stadium = 105

⇒ Number of male audience = (105 / 7) × 5 = 75

⇒ Number of female audience = (105 / 7) × 2 = 30

∴ The audience second stadium = 70

⇒ Number of male audience = (70 / 5) × 4 = 56

⇒ Number of female audience = (70 / 5) × 1 = 14

∴ The audience third stadium = 35

⇒ Number of male audience = (35 / 5) × 4 = 28

⇒ Number of female audience = (35 / 5) × 1 = 7

∵ For forth stadium the total audience for the match = 1 / 3 of first match audience + 1 / 2 of second match audience + 1 / 7 of third match

⇒ 1 / 3 of the first match audience then male audience = 75 × 1 / 3 = 25

⇒ 1 / 3 of the first match audience then female audience = 30× 1 / 3 = 10

⇒ 1 / 2 of the second match audience then male audience = 56 × 1 / 2 = 28

⇒ 1 / 2 of the second match audience then female audience = 14 × 1 / 2 = 7

⇒ 1 / 7 of the third match audience then male audience = 28 × 1 / 7 = 4

⇒ 1 / 7 of the third match audience then female audience = 7 × 1 / 7 = 1

Hence the total audience for fourth match = 25 + 10 + 28 + 7 + 4 + 1 = 75

Hence the female audience for fourth match = 10 + 7 + 1 =18

∴ Percent of female in the fourth match = (18 / 75) × 100 = 24%

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