In an army selection process, the ratio of selected to unselected candidates was 6 : 1. If 30 fewer candidates had applied and 10 fewer had been selected, then the ratio of selected to unselected candidates would have become 7 : 1. How many candidates had originally applied for the process?

Introduction / Context:
This is a classic selection and ratio problem involving total candidates, selected candidates and unselected candidates. It checks the ability to translate ratio statements into algebraic equations and then solve for the total number of participants. This type of question appears frequently in competitive exams to test reasoning with ratios, totals and hypothetical changes.

Given Data / Assumptions:

• Initial ratio of selected : unselected candidates = 6 : 1.
• If 30 fewer candidates had applied, the total would reduce by 30.
• If 10 fewer had been selected, the new selected count becomes original selected minus 10.
• Under these new conditions, the ratio selected : unselected becomes 7 : 1.
• We are asked to find the original number of candidates who applied.

Concept / Approach:
First, we express the original numbers of selected and unselected candidates in terms of a common variable using the ratio 6 : 1. That also gives us the original total number of candidates. Next, we adjust these numbers according to the hypothetical situation: subtract 30 from the total and 10 from the selected, and deduce the new unselected count from the new total. Using the new ratio 7 : 1, we get an equation in the variable. Solving this equation yields the original total number of applicants.

Step-by-Step Solution:

Verification / Alternative check:
Originally, selected = 6 * 130 = 780, unselected = 130. Ratio = 780 : 130 = 6 : 1 (correct). In new scenario: total = 910 - 30 = 880, selected = 780 - 10 = 770, unselected = 880 - 770 = 110. New ratio = 770 : 110 = 7 : 1, which matches the condition. So the answer 910 is confirmed.

Why Other Options Are Wrong:

• 1820, 455, and 2730 do not satisfy both ratio conditions when substituted.
• For example, if total = 455, selected and unselected would not yield the required new ratio of 7 : 1 after the described changes.

Common Pitfalls:
Some learners may incorrectly subtract 30 only from selected or only from unselected instead of from the total. Others may forget to recalculate the new unselected count from the new total and new selected. Keeping track of each adjusted number and carefully forming the ratio equation is essential to avoid mistakes.

Final Answer:
The original number of candidates who applied for the process is 910.