Question

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

Answer 1

Hint: Here we will set the values and store the values in variable. Assign the values and form the formula manually. We form formulas to take information in question. And we will substitute the values in that formula and we will get the answer.

Complete step-by-step answer:
Let the number of students in a group be $x$
If there are $3$ more students in a group, then
The total number of students in a group $ = x + 3$
According to the given problem.
$10 \times x = (x + 3) \times (10 - 2)$ (Here amount $ \times $ total number of students is $10 \times x$ and total number of student and minus the rupees values)
On simplification of values in above equation
$
\Rightarrow 10x = (x + 3) \times 8 \\
\Rightarrow 10x = 8x + 24 \\
\Rightarrow 10x - 8x = 24 \\
\Rightarrow 2x = 24 \\
\Rightarrow x = \dfrac{{24}}{2} \\
 $
We will get the answer,
$x = 12$
Therefore, the total number of students in the group =$12$.

Additional information:
To solve this kind of questions we need to note the following points: We can add a number with a variable to both sides without changing the equation or the values. We can subtract a number with a variable to both sides without changing the equation or the values. We can multiply a number with a variable to both sides without changing the equation or the values. We can divide a number with a variable to both sides without changing the equation or the values.

Note: When we want to solve a linear equation with variables on both sides, the first step is to isolate the variables to one side. Once we have done that, we can do subtraction, addition, cross multiplication, or any other necessary steps to solve the equation.