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In a town, every day, 20% people travel by bus, 25% travel by train, 10% travel by cab, 15% travel by metro and remaining stay at home. Assume that a person uses only one mode of transport. 75% of the women stay at home and 25% of the men stay at home. If 80% of the people that travel by train are males and remaining 2250 people in trains are females, what is the difference between the number of males and females in town?

In a town, every day, 20% people travel by bus, 25% travel by train, 10% travel by cab, 15% travel by metro and remaining stay at home. Assume that a person uses only one mode of transport. 75% of the women stay at home and 25% of the men stay at home. If 80% of the people that travel by train are males and remaining 2250 people in trains are females, what is the difference between the number of males and females in town? Correct Answer 36000

∵ 80% of the people that travel by train are males

∴ 20% of the people that travel by train are females

Number of people that travel by train = 2250 × (100/20) = 11250

Total number of people in town = 11250 × (100/25) = 45000

Percentage of people that stay at home = 100% − (20% + 25% + 10% + 15%) = 30%

Number of people who stay at home = (30/100) × 45000 = 13500

Let the number of males and females in town be ‘x’ and ‘y’, respectively.

∴ x + y = 45000      ---- (1)

∴ 25% of x + 75% of y = 13500

⇒ x/4 + 3y/4 = 13500

⇒ x + 3y = 54000      ---- (2)

Subtracting (1) from (2) gives,

2y = 9000

⇒ y = 4500

Putting in (1)

x = 45000 – 4500 = 40500

Required difference = 40500 – 4500 = 36000

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