Question

there are some coloured rubber bands in a box. ⅜ of them are blue, ¼ of them are red and ⅚ of the remainder are yellow. There are 20 yellow rubber bands. Find the total number of rubber bands in the box​

Answer 1

64

Explanation:

let rubber bands = x

blue bands = 3x/8

red bands = x/4

red and blue bands = 3x/8 + x/4

= (12x + 8x ) / 32

= 20x / 32

= 5x / 8

yellow bands = 5/6 of the remainder

= 5/6 (x - 5x/8)

= 5/6 (8x -5x / 8)

= 5/6 (3x/8)

= 5x / 16

as per question yellow bands = 20

thus,

20 = 5x / 16

20 * 16 = 5x

320 / 5 = x

x = 64

Answer 2

Let's start by finding the number of yellow rubber bands in the box:

If ⅜ of the rubber bands are blue, then 5/8 of them are not blue.

If ¼ of the rubber bands are red, then 3/4 of them are not red.

So, the total number of rubber bands in the box is 8/5 times the number of yellow rubber bands (since ⅚ of the remainder are yellow).

We know that there are 20 yellow rubber bands, so we can set up an equation: 8/5x = 20, where x is the total number of rubber bands in the box.

Solving for x, we get: x = 20 x 5/8 x 8/5 = 25.

Therefore, there are 25 rubber bands in the box.