The following Table-1 and Table-2

Show the breakup of 4170 vacant posts in six Banks A-F, and the percentage (%) breakup of the requirement of personnel in six different cadres in a Bank, namely, IT officers (ITO), Agricultural Field Officers (AFO), Law Officers (LO), Finance Executives (FE), Technical Officers (TO) and Probationary Officers (PO), respectively. Assume that these percentages are the same for all the six Banks. Based on the data in the tables, answer the questions.

Tables 1: Bank-wise Vacant Posts

Bank	Bank Number of Vacant Posts
A	800
B	940
C	600
D	820
E	450
F	560

Table 2:

Cadre in a Bank	Breakup (%)
ITO	11%
AFO	35%
LO	10%
FE	26%
TO	8%
PO	10

In Bank E, more TOS should be employed than the required number so that the ratio of

number of TOs to that of number of FEs becomes 2:3?

Correct Answer: The correct option is 42.

Step-by-step Explanation:

To find how many more Technical Officers (TOs) should be employed in Bank E, we must first calculate the current required number of TOs and Finance Executives (FEs) using the data provided in the tables.

Step 1: Identify the total vacant posts and relevant breakup percentages for Bank E
From Table 1, the total number of vacant posts in Bank E is 450.
From Table 2, the percentage breakup for the required cadres is:

• Finance Executives (FE) = 26%
• Technical Officers (TO) = 8%

Step 2: Calculate the required number of FEs and TOs in Bank E
First, calculate the required number of Finance Executives (FEs):

$$\text{Number of FEs}=26\%\text{of}450=\frac{26}{100}\times 450=117$$

Next, calculate the currently required number of Technical Officers (TOs):

$$\text{Number of TOs}=8\%\text{of}450=\frac{8}{100}\times 450=36$$

Step 3: Setup the equation for the new ratio
Let $x$ be the number of additional TOs that need to be employed.
The new number of TOs will be $36+x$.
We want the ratio of the number of TOs to the number of FEs to be 2:3. Therefore:

$$\frac{36+x}{117}=\frac{2}{3}$$

Step 4: Solve for $x$
Cross-multiplying the terms gives:

$$3\times (36+x)=2\times 117$$

$$108+3x=234$$

Subtracting 108 from both sides:

$$3x=234-108$$

$$3x=126$$

Dividing by 3:

$$x=\frac{126}{3}=42$$

Thus, 42 more TOs should be employed in Bank E.