Table given below shows ratio of books to pens sold by four different shops…
2021
Table given below shows ratio of books to pens sold by four different shops and it also shows average number of books and pens sold by these four shops.
Find the ratio of total pens sold by shop A to total books sold by shop C?
- A.
1 : 3
- B.
2 : 3
- C.
3 : 4
- D.
2 : 5
- E.
1 : 4
Attempted by 15 students.
Show answer & explanation
Correct answer: B
Concept
When a table gives a part-to-part ratio together with the average of the two quantities, recover the common multiplier from the average. If the two quantities are in ratio p : q, their sum is (p + q) parts and their average is (p + q)/2 parts. Setting that average equal to the given value fixes one part, after which any individual quantity is just its number of parts times the part value.
Application
Shop A — books : pens = 4 : 1, average of books and pens = 100. Let one part = a, so books = 4a and pens = a. Then (4a + a)/2 = 100, i.e. 5a/2 = 100, giving 5a = 200 and a = 40.
Pens sold by Shop A = 1 part = a = 40.
Shop C — books : pens = 2 : 3, average = 75. Let one part = c, so books = 2c and pens = 3c. Then (2c + 3c)/2 = 75, i.e. 5c/2 = 75, giving 5c = 150 and c = 30.
Books sold by Shop C = 2 parts = 2c = 60.
Required ratio = pens of A : books of C = 40 : 60. Dividing both terms by 20 gives 2 : 3.
Cross-check
Verify the averages: Shop A has books 160 and pens 40, average (160 + 40)/2 = 100 — matches. Shop C has books 60 and pens 90, average (60 + 90)/2 = 75 — matches. So pens of A : books of C = 40 : 60 = 2 : 3.