In a box, there are chocolate bars of 3 colours, purple, black and blue. There are 406 more black chocolate bars than blue chocolate bars. The number of blue chocolate bars is ¹₄ more than the purple chocolate bars. Given that the number of blue chocolate bars is 15% of the total number of chocolate bars in the box, how many more black chocolate bars are there than purple chocolate bars?

Purple chocolate bars	Black chocolate bars	Blue chocolate bars
	1 u + 406	1 u
4x3		5x3
85%		15%
12%	73%	15%

1 + ¹₄ = ⁴₄ + ¹₄ = ⁵₄

Yellow chocolate bars : Purple chocolate bars = 4 : 5

The number of blue chocolate bars is repeated.  Make the number of blue chocolate bars the same.

5 x 3 = 15%

Total number of purple chocolate bars and black chocolate bars in percent
= 100% - 15%
= 85%

Number of black chocolate bars in percent
= 85% - 12%
= 73%

Number of more black chocolate bars than blue chocolate bars in percent
= 73% - 12%
= 58%

58% = 406

1% = 406 ÷ 58 = 7

Number of more black chocolate bars than purple chocolate bars
= 73% - 12%
= 61%
= 61 x 7
= 427

Answer(s): 427