The ratio of saloon cars to the total number of cars on display in Ken's car shop was 4 : 11. ²₇ of the remaining cars on display were electric cars and the rest were family cars and sports cars in the ratio of 9 : 4. If there were 105 more saloon cars than family cars, how many sports cars were there?

Saloon Cars	Electric Cars	Family Cars	Sports Cars	Total Cars
4x13	7x13			11x13
	2x13	5x13		7x13
		9x5	4x5
52 u	26 u	45 u	20 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 5 and 13 is 65.

The total number of electric cars, family cars and sports cars is the next combined repeated identity. Make the total number of electric cars, family cars and sports cars the same. LCM of 7 and 7 is 91. 

Number of more saloon cars than family cars
= 52 u - 45 u
= 7 u

7 u = 105

1 u = 105 ÷ 7 = 15

Number of sports cars
= 20 u
= 20 x 15
= 300

Answer(s): 300