There are both boys and girls during a picnic. After fifteen girls have left, there is a 2:1 ratio of boys to girls left. Later, 45 boys depart, changing the ratio to 1:5. In the beginning, there were 8p girls and then value of p is-

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answer is B.

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Detailed Solution

Concept: The ratio between two amounts illustrates how many times one value is contained in the other through a quantitative relationship. In this case, a mile per hour is a comparison of miles and hours, and it is a means to compare two quantities by using the division method. It is a mathematical expression that is expressed as a: b, where a and b can be any two integers.
Let the initial ratio of boys to girls be

, with the initial number of girls being 8p, and the initial number of boys being q.
Since fifteen girls depart from the picnic, the equation is as follows:

The preceding equation can be expressed as follows:

Now that 45 lads have left the picnic, the ratio has changed from 2:1 to 1:5, making the ratio 1:5.

By cross multiplying, we get

Now equate equation

and

in terms of 8p−15 , we get