Question : In an army selection process, the ratio of selected to unselected was 5:1. If 100 fewer people had applied and 20 fewer had been selected, the ratio of selected to unselected candidates would have been 6 : 1. How many candidates had applied for the process?
Option 1: 5520
Option 2: 2760
Option 3: 1380
Option 4: 8280
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Correct Answer: 2760
Solution : Given: In an army selection process, the ratio of selected to unselected was $5:1$. Let the selected candidates be $5x$ and the unselected candidates be $x$. Total number of candidates = $5x + x = 6x$ Given: If 100 fewer candidates applied, 20 fewer were selected. ⇒ $6x - 100$ have been applied and $5x – 20$ have been selected. Total number of unselected candidates = Total number of applied candidates – Total selected candidates Total number of unselected candidates = $(6x – 100) – (5x – 20) = x – 80$ $\frac{\text{Selected Candidates}} {\text{Unselected Candidates}}= \frac{6}{1}$ ⇒ $\frac{(5x-20)}{(x-80)}= \frac{6}{1}$ ⇒ $5x – 20 = 6(x – 80)$ ⇒ $5x – 20 = 6x – 480$ ⇒ $6x – 5x = 480 – 20$ $\therefore x = 460$ Total number of candidates applied initially = $6x = 6 × 460 = 2760$ Hence, the correct answer is 2760.
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Question : In an army selection process, the ratio of selected to unselected candidates was $4:1$. If 90 fewer candidates had applied and 20 fewer were selected, the ratio of selected to unselected candidates would have been $5:1$. How many candidates had applied for the process?
Option 1: 1650
Option 2: 3300
Option 3: 825
Option 4: 4950
Question : In an army selection process, the ratio of selected to unselected candidates was 4 : 1. If 60 fewer candidates had applied and 20 fewer were selected, the ratio of selected to unselected candidates would have been 5 : 1. How many candidates had applied for the process?
Option 1: 1250
Option 3: 900
Option 4: 950
Question : Select the option that expresses the given sentence in passive voice.
The Indian army airlifted thousands of people from Ukraine.
Option 1: Thousands of people had been airlifted from Ukraine by the Indian army.
Option 2: Thousands of people have been airlifted from Ukraine by the Indian army.
Option 3: Thousands of people are airlifted from Ukraine by the Indian army.
Option 4: Thousands of people were airlifted from Ukraine by the Indian army.
Question : The ratio of the angles of a triangle is 1 : 2 : 6. What is the smallest angle?
Option 1: $40^\circ$
Option 2: $45^\circ$
Option 3: $30^\circ$
Option 4: $20^\circ$
Question : If the areas of two similar triangles are in the ratio 36 : 121, then what is the ratio of their corresponding sides?
Option 1: 6 : 11
Option 2: 11 : 5
Option 3: 6 : 5
Option 4: 5 : 12
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