Question

Rahul purchased \[7\] dvds each of which costs \[Rs.{\text{ }}17\]. He gave a five hundred rupee note to the shopkeeper. The amount returned to him is divisible by?

Answer 1

Hint: The cost of one dvd is given, we will find the cost of seven dvds by multiplying the cost of one dvd with seven i.e., \[\left( {7 \times Rs.{\text{ }}17} \right)\]. Then we will find the amount returned to Rahul by the shopkeeper which will be equal to the amount given by Rahul to the shopkeeper minus total costs of seven dvds i.e., \[\left[ {500 - \left( {7 \times Rs.{\text{ }}17} \right)} \right]\]. Then at last, we will find the number by which the amount returned is divisible.

Complete step by step solution:
Given, cost of one dvd \[ = \] \[Rs.{\text{ }}17\]
Since Rahul has purchased \[7\] dvds, we have to find the value of seven dvds from the given cost of one dvd.
\[ \Rightarrow \] Cost of \[7\] dvds\[ = \] Cost of \[1\] dvd \[ \times \] \[7\]
\[ \Rightarrow \] Cost of \[7\] dvds\[ = \]\[Rs.{\text{ }}17 \times 7\]
\[\therefore \]Cost of \[7\] dvds\[ = Rs.{\text{ 119}}\]
Rahul gave a five hundred rupee note to the shopkeeper, therefore the amount returned to Rahul by the shopkeeper will be equal to the amount given by Rahul to the shopkeeper minus total costs of seven dvds purchased by Rahul. Hence, we can write
Amount returned to Rahul \[ = Rs.{\text{ 500}} - Rs.{\text{ 119}}\]
\[\therefore \] Amount returned to Rahul \[ = Rs.{\text{ 381}}\]
We can see that \[{\text{381}}\] is divisible by \[{\text{3}}\].
On dividing \[{\text{381}}\] by \[{\text{3}}\] we get \[127\] i.e., \[381 \div 3 = 127\], which is a prime number. A prime number is a positive number which has only two factors i.e., \[1\] and itself.
Hence, the amount returned to Rahul is divisible by \[{\text{3}}\] and \[127\].
So, the correct answer is “\[{\text{3}}\] and \[127\]”.

Note: Here, on division by \[{\text{3}}\] we got a prime number, but in cases where on division we do not get a prime number for those cases we will get multiple answers. For such situations we have to give the answer accordingly whether the question has asked the smallest divisible number, largest divisible number and so on.