Question

Here is a key board of a harmonium:

1. Find the ratio of white keys to black keys on the keyboard.
   
2. What is the ratio of black keys to all keys on the given keyboard.
3. This pattern of keys is repeated on larger keyboard. How many black keys would you expect to find on a keyboard with 14 such patterns.

Answer 1

According to the given figure,

a. The total number of black keys = 7

The total number of white keys = 10

Hence, the ratio of white keys to black keys on the keyboard = `10/7`

b. The total number of all keys = 10 + 7 = 17

The ratio of black keys to all keys on the given keyboard = `7/17`

c. Black keys in 1 keyboard = 7

Black keys in 14 such keyboards = 14 × 7 = 98 keys.