A question is given, followed by three statements labelled I, II and III. Identify which of the statements is/are sufficient to answer the question.

Question:

What is the daily wages (in ₹) of one worker of type A?

Statements:

I. In a factory, the ratio of the number of workers of type A, B and C is 9 : 4 :1 and the ratio of daily wages of one worker of type A, B and C is 8 : 5 : 3. Total daily wages of all workers of type A, B and C is ₹57,000.

II. The number of workers of type B is 20.

III. The number of workers of type C is 5.

Correct option is A

Given:

​Question:
What is the daily wages (in ₹) of one worker of type A?

Statements:
I. In a factory, the ratio of the number of workers of type A, B and C is 9 : 4 :1 and the ratio of daily wages of one worker of type A, B and C is 8 : 5 : 3. Total daily wages of all workers of type A, B and C is ₹57,000.
II. The number of workers of type B is 20.
III. The number of workers of type C is 5.

Solution:

Statement I:
Ratio of workers A : B : C = 9 : 4 : 1
Ratio of daily wages A : B : C = 8 : 5 : 3
Total daily wages of all A, B, and C workers = ₹57,000

Let:
Number of A workers = 9x
B workers = 4x
C workers = x
Let daily wage of A = ₹8y, B = ₹5y, C = ₹3y
$$\text{Total daily wages} = ₹57,000 \\\Rightarrow 9x \cdot 8y + 4x \cdot 5y + x \cdot 3y = 57000 \\\Rightarrow 72xy + 20xy + 3xy = 57000 \Rightarrow 95xy = 57000 \\\ \\\Rightarrow xy = \frac{57000}{95} = 600 \\\text{We only know the product } xy, \text{ so this alone is not sufficient.}$$

$$\textbf{Statement II:} \\\text{Number of type B workers} = 20 \Rightarrow 4x = 20 \Rightarrow x = 5 \\\text{From earlier: } xy = 600 \Rightarrow y = \frac{600}{5} = 120 \\\ \\\text{Wage of A} = 8y = 8 \times 120 = \boxed{₹960}\\[10pt]\textbf{Statement III:} \\\text{Number of type C workers} = 5 \Rightarrow x = 5 \\\text{Then again: } y = \frac{600}{5} = 120\\ \Rightarrow \text{Wage of A} = 8 \times 120 = \boxed{₹960}$$

Statement II or III alone won’t help without I, since they don’t tell us anything about ratios or total wages.
Final Answer: (A) I and II or I and III​​​​