Quantitative Aptitude and Reasoning Archives

201. By selling an article for ₹ 2700, a man loses 10%. If he sells it for

By selling an article for ₹ 2700, a man loses 10%. If he sells it for ₹ 3600, his gain per cent is

[amp_mcq option1=”15″ option2=”18″ option3=”20″ option4=”25″ correct=”option3″]

This question was previously asked in

UPSC CAPF – 2019

The correct answer is C) 20.

Let the Cost Price (CP) of the article be ₹ x.
When sold for ₹ 2700, there is a loss of 10%.
Selling Price (SP) = CP * (1 – Loss Percentage / 100)
2700 = x * (1 – 10/100)
2700 = x * (1 – 0.10)
2700 = x * 0.90
x = 2700 / 0.90 = 27000 / 9 = ₹ 3000.
So, the Cost Price of the article is ₹ 3000.
Now, if the article is sold for ₹ 3600, the Selling Price is ₹ 3600.
The gain is SP – CP = 3600 – 3000 = ₹ 600.
The gain percentage is (Gain / CP) * 100.
Gain percentage = (600 / 3000) * 100 = (6 / 30) * 100 = (1 / 5) * 100 = 20%.

The formula for SP with loss is SP = CP * (100 – Loss%) / 100.
The formula for SP with gain is SP = CP * (100 + Gain%) / 100.
Gain percentage is (Gain / CP) * 100.

202. In a test consisting of 150 questions, Neha answered 40% of the first

In a test consisting of 150 questions, Neha answered 40% of the first 90 questions correctly. What per cent of the 60 questions does she need to answer correctly for her score in the entire test to be 60% ?

[amp_mcq option1=”75″ option2=”80″ option3=”85″ option4=”90″ correct=”option4″]

This question was previously asked in

UPSC CAPF – 2019

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The correct answer is D) 90.

The total number of questions in the test is 150. Neha wants to score 60% in the entire test, which means she needs to answer 60% of 150 questions correctly.
Total correct answers required = 0.60 * 150 = 90.
In the first 90 questions, she answered 40% correctly.
Number of correct answers in the first 90 questions = 0.40 * 90 = 36.
The number of remaining questions is 150 – 90 = 60.
To achieve a total of 90 correct answers, she needs an additional 90 – 36 = 54 correct answers from the remaining 60 questions.
The percentage of correct answers needed from the remaining 60 questions is (Number of correct answers needed / Total remaining questions) * 100.
Percentage = (54 / 60) * 100 = (9 / 10) * 100 = 90%.

This is a basic percentage calculation problem involving weighted averages implicitly. The overall percentage is a weighted average of percentages in segments of the test.

203. If the numerator of a fraction is increased by 200% and the denodminat

If the numerator of a fraction is increased by 200% and the denodminator is increased by 300%, the resultant fraction is 9/17. What was the original fraction ?

[amp_mcq option1=”10/17″ option2=”11/17″ option3=”12/17″ option4=”13/17″ correct=”option3″]

This question was previously asked in

UPSC CAPF – 2019

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Let the original fraction be represented as n/d, where n is the numerator and d is the denominator.
The numerator is increased by 200%. This means the new numerator is the original numerator plus 200% of the original numerator.
New numerator = n + 200% of n = n + (200/100) * n = n + 2n = 3n.
The denominator is increased by 300%. This means the new denominator is the original denominator plus 300% of the original denominator.
New denominator = d + 300% of d = d + (300/100) * d = d + 3d = 4d.
The resultant fraction is the new numerator divided by the new denominator: (3n) / (4d).
We are given that the resultant fraction is 9/17.
So, (3n) / (4d) = 9/17.
We need to find the original fraction n/d. We can rearrange the equation to solve for n/d:
(3/4) * (n/d) = 9/17
Multiply both sides by the reciprocal of (3/4), which is (4/3):
n/d = (9/17) * (4/3)
n/d = (9 * 4) / (17 * 3)
n/d = 36 / 51
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
36 / 3 = 12
51 / 3 = 17
So, the original fraction was 12/17.

When a quantity is increased by X%, the new quantity is the original quantity plus X% of the original quantity, which is equivalent to Original Quantity * (1 + X/100). In this case, a 200% increase means the new value is (1 + 200/100) = 3 times the original. A 300% increase means the new value is (1 + 300/100) = 4 times the original.

Algebraic representation of word problems is key. Setting up the equation correctly based on the given percentages and the resulting fraction allows one to solve for the unknown original fraction. Simplifying the final fraction to its lowest terms is standard practice.

204. One-sixth of a number is 53. What will be 57% of that number ?

One-sixth of a number is 53. What will be 57% of that number ?

[amp_mcq option1=”136.74″ option2=”149.46″ option3=”181.26″ option4=”197.16″ correct=”option3″]

This question was previously asked in

UPSC CAPF – 2019

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Let the number be N.
According to the problem, one-sixth of the number is 53.
(1/6) * N = 53
To find the number N, multiply both sides by 6:
N = 53 * 6
N = 318
Now, we need to find 57% of this number.
57% of N = 57/100 * N
57% of 318 = 0.57 * 318
Calculation:
0.57 * 318 = (0.5 + 0.07) * 318
= (0.5 * 318) + (0.07 * 318)
= 159 + (0.07 * 300) + (0.07 * 18)
= 159 + 21 + 1.26
= 180 + 1.26
= 181.26
Alternatively:
318 * 57 = 318 * (60 – 3) = 318 * 60 – 318 * 3
318 * 6 = 1908, so 318 * 60 = 19080
318 * 3 = 954
19080 – 954 = 18126
Since it’s 0.57, we need to place the decimal two places from the right.
Result = 181.26

The problem involves two steps: first, finding the original number given a fraction of it, and second, calculating a percentage of that number.

Percentage calculations are common in quantitative aptitude. Remember that x% of a number is (x/100) multiplied by the number. Fractions and percentages are interconvertible forms of representing parts of a whole.

205. In this item, four words have been given, out of which three are alike

In this item, four words have been given, out of which three are alike in some manner and the fourth one is different. Choose the odd one out.

[amp_mcq option1=”Friendship” option2=”Intimacy” option3=”Attachment” option4=”Enmity” correct=”option4″]

This question was previously asked in

UPSC CAPF – 2019

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The given words are Friendship, Intimacy, Attachment, and Enmity.
Friendship: A relationship between friends.
Intimacy: Close familiarity or friendship.
Attachment: A feeling of fondness or loyalty for a person or place.
Enmity: The state or feeling of being actively opposed or hostile to someone or something.
Friendship, Intimacy, and Attachment all describe positive emotional connections or bonds between people. Enmity, however, describes a state of hostility or strong dislike, which is the opposite of the feelings represented by the other three words. Therefore, Enmity is the odd one out.

Odd one out questions require identifying a common characteristic or relationship shared by three items and finding the one item that does not share that characteristic or is opposite in nature. Understanding the meaning of the words is essential.

These questions test vocabulary and the ability to identify semantic relationships between words. Categories can be based on type, function, properties, antonyms/synonyms, etc.

206. If in a certain language GAMBLE is coded as FBLCKF, how is FLOWER code

If in a certain language GAMBLE is coded as FBLCKF, how is FLOWER coded in that language ?

[amp_mcq option1=”GMPVDS” option2=”GKPVFQ” option3=”EMNXDS” option4=”EMNTDS” correct=”option3″]

This question was previously asked in

UPSC CAPF – 2019

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The given coding is GAMBLE -> FBLCKF. Let’s analyze the letter transformations:
G (7) -> F (6): -1
A (1) -> B (2): +1
M (13) -> L (12): -1
B (2) -> C (3): +1
L (12) -> K (11): -1
E (5) -> F (6): +1
The pattern is an alternating subtraction and addition of 1 to the alphabetical position of each letter: -1, +1, -1, +1, -1, +1.
Now apply this pattern to the word FLOWER:
F (6) -> F-1 = E (5)
L (12) -> L+1 = M (13)
O (15) -> O-1 = N (14)
W (23) -> W+1 = X (24)
E (5) -> E-1 = D (4)
R (18) -> R+1 = S (19)
The coded word for FLOWER is EMNXDS.

Coding-Decoding problems often involve identifying patterns based on the position of letters in the alphabet, skipping letters, or reversing the sequence. Analyzing the transformation for each letter from the original word to the coded word is the first step.

Understanding the alphabetical order and assigning numerical values (A=1, B=2, …) can facilitate identifying patterns based on addition or subtraction. Sometimes the pattern can be more complex, involving skipping letters, using reverse alphabetical order, or rearranging letters.

207. If M is brother of N, B is brother of N and M is brother of D, then wh

If M is brother of N, B is brother of N and M is brother of D, then which one of the following statements is definitely true ?

[amp_mcq option1=”N is brother of B” option2=”N is brother of M” option3=”N is brother of D” option4=”M is brother of B” correct=”option4″]

This question was previously asked in

UPSC CAPF – 2019

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The relationships given are: M is brother of N, B is brother of N, and M is brother of D.
From “M is brother of N” and “B is brother of N”, we know that M and B are siblings of N.
From “M is brother of D”, we know that M is a sibling of D.
Since M is a sibling of N and also a sibling of D, N and D must also be siblings of M. Thus, M, N, B, and D are all siblings.
M and B are explicitly stated as brothers, meaning they are male. The genders of N and D are not explicitly stated.
Let’s examine the options:
A) N is brother of B: Not necessarily true, N could be female (sister).
B) N is brother of M: Not necessarily true, N could be female (sister).
C) N is brother of D: Not necessarily true, N could be female (sister).
D) M is brother of B: Since M and B are both siblings of N (M is brother of N, B is brother of N), they must be siblings of each other. M is stated as male (“brother”), so M is indeed the brother of B. This statement is definitely true.

In blood relation problems, accurately mapping the relationships and genders (where specified) is crucial. Identifying common relatives helps establish connections between individuals not directly linked in the initial statements. The term “sibling” implies being a brother or sister. “Brother” implies male gender.

Using diagrams or symbols (e.g., square for male, circle for female, vertical line for parent-child, horizontal line for siblings) can help visualize the relationships and avoid confusion, especially in more complex problems. When a person’s gender is not specified (e.g., just “sibling”), their gender cannot be assumed.

208. There are five friends – Sachin, Kunal, Mohit, Amit and Sohan. Sachin

There are five friends – Sachin, Kunal, Mohit, Amit and Sohan. Sachin is shorter than Kunal but taller than Sohan. Mohit is the tallest. Amit is little shorter than Kunal and little taller than Sachin. If they stand in the order of increasing heights, who will be the third ?

[amp_mcq option1=”Amit” option2=”Sohan” option3=”Sachin” option4=”Kunal” correct=”option1″]

This question was previously asked in

UPSC CAPF – 2019

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Let’s represent the heights:
1. Mohit is the tallest (M > others).
2. Sachin is shorter than Kunal but taller than Sohan (K > Sachin > Sohan).
3. Amit is little shorter than Kunal and little taller than Sachin (K > Amit > Sachin).
Combining these, we have:
– M is the tallest.
– We know K > Amit and Amit > Sachin. We also know K > Sachin and Sachin > Sohan.
Putting it all together in increasing order (shortest to tallest): Sohan < Sachin < Amit < Kunal < Mohit. If they stand in the order of increasing heights, the sequence is Sohan, Sachin, Amit, Kunal, Mohit. The third person is Amit.

This is a logic puzzle requiring careful analysis of relative comparisons to establish a complete order.

The phrasing “little shorter” and “little taller” are qualitative descriptions but confirm the relative positions established by the inequalities (K > Amit and Amit > Sachin). The core task is to sequence the five individuals based on the given pairwise comparisons.

209. A walks 10 metres in front and 10 metres to the right. Then every time

A walks 10 metres in front and 10 metres to the right. Then every time turning to his left he walks 5, 15 and 15 metres respectively. How far is he now from his starting point ?

[amp_mcq option1=”55 metres” option2=”23 metres” option3=”5 metres” option4=”None of these” correct=”option3″]

This question was previously asked in

UPSC CAPF – 2019

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The person is 5 metres away from their starting point.

The problem can be solved by tracking the person’s displacement in two perpendicular directions (e.g., North-South and East-West).

Assume ‘front’ is North.
1. 10 metres in front (North): Displacement (0, +10)
2. 10 metres to the right (East from the North direction): Displacement (+10, 0)
Total displacement so far: (+10, +10) from start. Current position is (10, 10) relative to start (0, 0). Direction is East.
3. Turning left (now facing North) walks 5 metres: Displacement (0, +5).
Total displacement: (+10, +10) + (0, +5) = (+10, +15). Current position (10, 15). Direction is North.
4. Turning left (now facing West) walks 15 metres: Displacement (-15, 0).
Total displacement: (+10, +15) + (-15, 0) = (-5, +15). Current position (-5, 15). Direction is West.
5. Turning left (now facing South) walks 15 metres: Displacement (0, -15).
Total displacement: (-5, +15) + (0, -15) = (-5, 0). Current position (-5, 0).
The starting point is (0, 0). The final position is (-5, 0).
The distance from the starting point is the straight-line distance between (0, 0) and (-5, 0), which is 5 metres.

210. If the first day of the year (other than the leap year) was Sunday, th

If the first day of the year (other than the leap year) was Sunday, then which was the last day of that year ?

[amp_mcq option1=”Monday” option2=”Sunday” option3=”Saturday” option4=”None of these” correct=”option2″]

This question was previously asked in

UPSC CAPF – 2019

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If the first day of a non-leap year is a Sunday, the last day of that year is also a Sunday.

A non-leap year has 365 days. The number of days in a year is 365.

To determine the day of the week for the last day of the year relative to the first day, we can find the number of days modulo 7.
$365 \div 7 = 52$ with a remainder of $1$.
This means 365 days consist of 52 full weeks and 1 additional day.
If the first day is Sunday (Day 1), the day after 52 full weeks (which is Day $1 + 52 \times 7 = 1 + 364 = 365$) will be the same day as the first day.
So, if Day 1 is Sunday, Day 365 is Sunday.