The ratio of family 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 electric cars and sports cars in the ratio of 8 : 5. If there were 210 more family cars than electric cars, how many sports cars were there?

Family Cars	Saloon Cars	Electric Cars	Sports Cars	Total Cars
2x13	3x13			5x13
	1x13	2x13		3x13
		8x2	5x2
26 u	13 u	16 u	10 u

The total number of electric cars and sports cars is the combined repeated identity. Make the total number of electric cars and sports cars the same. LCM of 2 and 13 is 26.

The total number of saloon cars, electric cars and sports cars is the next combined repeated identity. Make the total number of saloon cars, electric cars and sports cars the same. LCM of 3 and 3 is 39. 

Number of more family cars than electric cars
= 26 u - 16 u
= 10 u

10 u = 210

1 u = 210 ÷ 10 = 21

Number of sports cars
= 10 u
= 10 x 21
= 210

Answer(s): 210