Question

In a bookshop, the average number of biology, chemistry and physics books is 360. The biology books are 180 more than the average number of chemistry and physics books. The number of physics books is 180 less than the average of biology and chemistry books. What is the number of chemistry books in the shop?
1. 420
2. 540
3. 480
4. 360

Answer 1

Correct Answer - Option 4 : 360

Given:

Average number of biology, chemistry and physics books = 360.

Biology books = 180 + average number of chemistry and physics books.

Physics books = Average of biology and chemistry books - 180

Calculations:

Let the number of biology, chemistry and physics books be x, y and z.

(x + y + z)/3 = 360

⇒ x + y + z = 1080      ----(i)

Biology books = 180 + average number of chemistry and physics books,

x = 180 + (y + z)/2

⇒ 2x = 360 + y + z

⇒ 2x - y - z = 360      ----(ii)

Physics = Average of biology and chemistry books - 180,

z = (x + y)/2 - 180

⇒ 2z = x + y - 360

⇒ x + y - 2z = 360      ----(iii)

Adding equation (i) and (iii) and subtracting (iii),

(x + y + z) + (x + y - 2z) - (2x - y - z) = 1080 + 360 - 360

⇒ 2x + 2y - z - 2x + y + z = 1080

⇒ 3y = 1080

⇒ y = 360

∴ The number of chemistry books in the shop is 360.