Question

On a school picnic, a group of students agrees to pay equally for the use of a full boat and pay rupees $\;10$ each. If there had been 3 more students in the group, each would have paid rupees $2$ less. How many students were there in the group?

Answer 1

Hint: At first, we will take the number of students in the group as a variable $x$ . Here one thing is constant: that is the total cost. Then we will create an equation from the given information and then solve it. In this way, we will get the number of students.

Complete step-by-step solution:
Let the total number of students in the group is $x$ .
If each of the students agrees to pay equally for the use of a full boat and pay rupees $\;10$ then the total cost to use the boat is $10\;x$ .
Now, this is given that if there had been $3$ more students in the group, i.e. $(3 + x)$ students in the group they have to pay rupees $2$ less.
So each of them has to pay $10 - 2 = 8$ rupees.
So again we get the total cost is $(3 + x) \times 8$ .
Now the total cost to use the boat is constant so both of the costs must be equal.
So we get;
$10x = (3 + x) \times 8$
After multiplying we get;
$\Rightarrow 10x = 24 + 8x$
After subtracting $8\;x$ from both side we get;
$\Rightarrow 2x = 24$
After dividing $2$ from both side we get;
$\Rightarrow x = 12$

So the total number of students in the group is $\;12$.

Note: In this type of question at first, we have to see what the question wants to know. We will choose some variables as the wanted question. Then we have to find out the constant part of the question which may have been given or not given. Then we have to construct an equation concerning the constant and the variable and then we will get the value of the unknown variable.