**Sparkles Jewellery Shop sold diamonds, rubies and emeralds. 3/5 of the gemstones were diamonds. There were 168 fewer rubies than diamonds. The ratio of the number of rubies to the number of emeralds was 7:3. After some rubies were sold, 30% of the remaining gemstones in the shop were rubies and emeralds.a) How many rubies were sold?b) Find the percentage decrease in the number of gemstones. Leave your answer as a fraction.**

**Solution**

Rubies --> 7/10 of 2/5 = 14/50

Diamonds - Rubies --> 168 (more diamonds than rubies)

3/5 - 14/50 = 168

16/50 --> 168

1/50 --> 168 divided by 16 = 10.5

Rubies + Emeralds (2/5 of whole)

20/50 --> 20 x 10.5 = 210

2/5 of whole --> 210

1/5 of whole --> 210 divided by 2 = 105

(Diamonds) 3/5 of whole --> 3 x 105 = 315

After selling, Rubies and Emeralds make up 30%, while Diamonds make up 70%.

Diamonds 70% --> 315

10% --> 315 divided by 7 = 45

Rubies and Emeralds 30% --> 3 x 45 = 135

**(a)**

(Rubies and Emeralds before selling) - (Rubies and Emeralds after selling)

--> 210 - 135 = 75

**Answer: 75 rubies**

(b)

(b)

Percentage decrease in number of gemstones

1/50 of gemstones --> 10.5

50/50 of gemstones -> 50 x 10.5 = 525

75 rubies sold

--> (75/525) x 100% = 14 and 2/7 %

Answer: 14 and two-sevenths %

Answer: 14 and two-sevenths %