A student bought 4 books for Rs.120 from one book shop and 6 books for Rs.150 from another. The average price (in rupees), he paid per book was:
VerifiedHint: An average is a single number taken as representative of a list of numbers.
The average is the sum of the numbers divided by how many numbers are being averaged.
Here, the student bought some books from one shop and some from another shop.
We need to calculate the total amount by multiplying the number of books and the amount of price of one book for first and second both the shops. Then we will add both of them and divide them by the total number of books the student purchased from the first and second shops.
Complete step by step solution:
It is given that, the student bought 4 books for $Rs.120$ from one book shop and $6$ books for $Rs.150$ from another.
So for the first shop,
Number of books $=4$
The price per book is $=Rs.120$
Total amount of books he bought from the first shop is \[ = {\rm{ }}Rs.(120 \times 4) = Rs.480\]
For the second shop,
Number of books $=6$
The price per book is $=Rs.150$
Total amount of books he bought from the second shop is\[\; = {\rm{ }}Rs.(150 \times 6) = Rs.900\].
Hence the total amount of books he bought from both the shop is \[Rs.{\rm{ }}480 + 900 = Rs.1380\].
Total number of books the student purchased from first and second shop $=4+6=10$
The average price he paid per book is found by dividing the total amount by the number of books
That is the average price =\[\dfrac{{1380}}{{10}} = Rs.138\]
$\therefore$ The average price (in rupees), he paid per book was \[Rs.138\].
Note:
Here we can find the solution in a single step that is given by,
The average price of books \[ = \dfrac{{4(120) + 6(150)}}{{4 + 6}}\]
Which on solving we get,
The average price of books \[ = \dfrac{{480 + 900}}{{10}} = \dfrac{{1380}}{{10}} = 138\]
Hence the average price of $10$ books is \[Rs.138\]
