Question

Leela invited some friends on tea on her birthday. Her mother placed some puris on the table to be served. If leela places 4 puris in each plate then one plate remains empty. But if she places 3 puris in each plate then one puri is left behind. Find the number of plates and the number of puris on the table.

Answer 1

Hint: his problem can be solved best by assuming the number of plates to be a variable in each of the two conditions. Then equate the two equations formed and solve for x.

Complete step-by-step answer:
Let the number of plates on the table be $x$
There are 2 cases given for the puris which are served. Let’s see the cases one by one.
Case-1
If 4 puris are served, then one plate is empty
It means that $\left( {x - 1} \right)$ plates have 4 puris on them while the last one is empty.
The number of puris in $\left( {x - 1} \right)$ plates or the number of puris served on the table are,
$P = 4\left( {x - 1} \right) \cdots \left( 1 \right)$

Case-2
If 3 puris are served, then one puri is left behind.
It means that $x$ plates have 3 puris on them while the one puri is extra on the table.
The number of puris in plates plus one extra puri or the number of puris served on the table are,
$P = 3x + 1 \cdots \left( 2 \right)$
But the number of puris in the two cases should be equal. Therefore, the equation (1) and equation (2) should be equal.
Equating (1) and equation (2),
$4\left( {x - 1} \right) = 3x + 1$
Now solving the equation to obtain the number of plates on the table as,
$
  4x - 4 = 3x + 1 \\
  4x - 3x = 5 \\
  x = 5 \\
 $
The number plates on the table is $x = 5$ .
Substitute the value of $x = 5$ in equation (1) to obtain the number of puris which are served on the table as,
$
  P = 4\left( {5 - 1} \right) \\
  P = 16 \\
 $
Thus, the number puris is 16.
Now let’s check whether the answer is correct or not.
If 4 puris are served on each plate , then 4 plates will have 4 puris while the 5th plate will be empty.
Number of puris served on 4 plates are , $P = 4 \times 4 = 16$
If 3 puris are served on each plate then all plates have $3 \times 5 = 15$ puris among them and one puri is left.
Hence, our answer is correct as the condition is satisfied.

Note: The important point which should be kept in mind is that it is a problem which deals with a single variable only.The number of plates should be assumed to be a variable.Also, the number of puris should be written in terms of number plates.