The ratio of electric cars to the total number of cars on display in Ken's car shop was 2 : 5. ¹₃ of the remaining cars on display were saloon cars and the rest were family cars and sports cars in the ratio of 10 : 9. If there were 324 more electric cars than family cars, how many sports cars were there?

Electric Cars	Saloon Cars	Family Cars	Sports Cars	Total Cars
2x19	3x19			5x19
	1x19	2x19		3x19
		10x2	9x2
38 u	19 u	20 u	18 u

The total number of family cars and sports cars is the combined repeated identity. Make the total number of family cars and sports cars the same. LCM of 2 and 19 is 38.

The total number of saloon cars, family cars and sports cars is the next combined repeated identity. Make the total number of saloon cars, family cars and sports cars the same. LCM of 3 and 3 is 57. 

Number of more electric cars than family cars
= 38 u - 20 u
= 18 u

18 u = 324

1 u = 324 ÷ 18 = 18

Number of sports cars
= 18 u
= 18 x 18
= 324

Answer(s): 324