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 difference between average number of books sold by A & C and total pens sold by B?
- A.
10
- B.
5
- C.
15
- D.
25
- E.
20
Attempted by 1 students.
Show answer & explanation
Correct answer: E
Concept
In a data-interpretation set that gives a ratio of two quantities together with the AVERAGE of those same two quantities, you recover each quantity from two facts: (1) the average of two items equals their sum divided by 2, so the combined total is the average multiplied by 2; and (2) a ratio a : b splits that total into parts a/(a+b) and b/(a+b).
Application
Apply both facts to each required shop:
Shop A: total = 100 x 2 = 200; ratio books : pens = 4 : 1, so books = 200 x 4/5 = 160.
Shop B: total = 60 x 2 = 120; ratio books : pens = 1 : 3, so pens = 120 x 3/4 = 90.
Shop C: total = 75 x 2 = 150; ratio books : pens = 2 : 3, so books = 150 x 2/5 = 60.
Average books of A and C = (160 + 60) / 2 = 110.
Required difference = 110 - 90 = 20.
Cross-check
Re-add the parts as a check: for A, 160 books + 40 pens = 200 = 100 x 2; for B, 30 books + 90 pens = 120 = 60 x 2; for C, 60 books + 90 pens = 150 = 75 x 2. Every total matches its given average, so the books figures 160 and 60 and the pens figure 90 are reliable, giving the difference 20.