In a province, the cities are divided into 3 categories, A, B and C. The ratio of number of cities of type A and B is 6 : 11, while that of cities of type B and C is 3 : 43. If the number of cities of type A is 918, then what is the total number of cities in province?
The ratio of number of cities of type A and B is 6 : 11, while that of cities of type B and C is 3 : 43.
LCM of 11 and 3 is 33.
Combined ratio of cities of type A, B and C will be 18 : 33 : 473.
Let number of cities of type A, B and C be 18T, 33T and 473T, respectively.
So, 18T = 918
⇒ T = 51
∴ Total number of cities = 18T + 33T + 473T = 524 × 51 = 26724