In a box, there are chocolate bars of 3 colours, black, yellow and gold. There are 392 less gold chocolate bars than yellow chocolate bars. The number of gold chocolate bars is ¹₃ more than the black chocolate bars. Given that the number of gold chocolate bars is 16% of the total number of chocolate bars in the box, how many less black chocolate bars are there than yellow chocolate bars?

Black chocolate bars	Yellow chocolate bars	Gold chocolate bars
	1 u + 392	1 u
3x4		4x4
84%		16%
12%	72%	16%

1 + ¹₃ = ³₃ + ¹₃ = ⁴₃

Yellow chocolate bars : Purple chocolate bars = 3 : 4

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

4 x 4 = 16%

Total number of black chocolate bars and yellow chocolate bars in percent
= 100% - 16%
= 84%

Number of yellow chocolate bars in percent
= 84% - 12%
= 72%

Number of more yellow chocolate bars than gold chocolate bars in percent
= 72% - 12%
= 56%

56% = 392

1% = 392 ÷ 56 = 7

Number of less black chocolate bars than yellow chocolate bars
= 72% - 12%
= 60%
= 60 x 7
= 420

Answer(s): 420