The ratio of grade A officers and grade B officers is 3 : 7, and that of grade B and grade C officers is 2 : 5. If the total number of officers is 1375, then find the number of grade A officers?

A 100

B 125

C 150

D 180

E 200

Correct Answer: Option C

The ratio of grade A officers and grade B officers is 3 : 7, and that of grade B and grade C officers is 2 : 5.

Factor for grade B officers in two ratios are 7 and 2. We can take 14 as common factor.

⇒ Ratio of grade A, B and C officers will be 6 : 14 : 35.

Let number of grade A, B and C officers be 6T, 14T and 35T, respectively.

⇒ 6T + 14T + 35T = 1375

⇒ T = 1375/55 = 25

∴ Number of grade A officers = 6T = 6 × 25 = 150