A camp has provisions for 51 persons for 12 days. If the number of persons is increased to 102, for how many days will the same provisions last?

Correct Answer: 6

Step-by-Step Explanation:

To solve this problem, we need to understand the relationship between the number of persons and the number of days the provisions will last.

Since the total amount of provisions remains constant, an increase in the number of persons will cause the provisions to last for a fewer number of days. This is an example of an inverse proportion.

In an inverse proportion, the product of the two quantities remains constant. That is:

$P_1\times D_1=P_2\times D_2$

Where:
• $P_1$ = Initial number of persons = 51
• $D_1$ = Initial number of days = 12
• $P_2$ = New number of persons = 102
• $D_2$ = New number of days (which we need to find)

Now, substitute the given values into the equation:

$51\times 12=102\times D_2$

Solve for $D_2$:

$D_2=\frac{51\times 12}{102}$

Simplify the fraction:

$D_2=\frac{612}{102}=6$

Therefore, if the number of persons is increased to 102, the same provisions will last for 6 days.