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The District Transport Authority has started special bus services for college going students. One bus starts from village P. The number of girls in the bus is one-fourth of the number of boys. In village Q, 20 boys leave the bus at their college stop and ten girls enter the bus. Now the number of boys and girls is equal. How many students enter the bus in the beginning?

The District Transport Authority has started special bus services for college going students. One bus starts from village P. The number of girls in the bus is one-fourth of the number of boys. In village Q, 20 boys leave the bus at their college stop and ten girls enter the bus. Now the number of boys and girls is equal. How many students enter the bus in the beginning? Correct Answer 50

Let,

Number of girls = G

Number of boys = B

At village P

Number of girls in the bus is one-fourth of the number of boys so,

=> G = 1/4B

=> 4G = B

At village Q

20 boys leave the bus at their college stop and ten girls enter the bus.

Number of girls = G + 10

Number of boys = B - 20

Now the number of boys and girls is equal

=> G + 10 = B – 20

∵ 4G = B

So,

=> G + 10 = 4G – 20

=> 4G - 4 = 20 + 10

=> 3G = 30

=> G = 10

∵ 4G = B

So, B = 4 × 10

B = 40

Total number of students enter the bus in the beginning = B + G = 10 + 40 = 50

Hence, Total number of students enter the bus in the beginning is “50”.

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