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Arithmetical Reasoning MCQs for UPPSC (UP) Exam
It covers all Important Questions with answers on Arithmetical Reasoning for the UPPSC (UP) exam. The questions are based on important topics. Details about the questions:- Topic: Arithmetical Reasoning
- Type of Questions: MCQs with solutions
- Number of Questions: 24
- You can attempt them on EduRev to score high in UPPSC (UP) exam.
A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair?- a)3
- b)20
- c)39
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair?
a)
3
b)
20
c)
39
d)
None of these
 | Puneet Sharma answered |
Why 3???
while taking out socks may be all 3 are if same colour
while taking out socks may be all 3 are if same colour
Mac has £ 3 more than Ken, but then Ken wins on the horses and trebles his money, so that he now has £ 2 more than the original amount of money that the two boys had between them. How much money did Mac and Ken have between them before Ken's win?- a)£ 9
- b)£ 11
- c)£ 13
- d)£ 15
Correct answer is option 'C'. Can you explain this answer?
Mac has £ 3 more than Ken, but then Ken wins on the horses and trebles his money, so that he now has £ 2 more than the original amount of money that the two boys had between them. How much money did Mac and Ken have between them before Ken's win?
a)
£ 9
b)
£ 11
c)
£ 13
d)
£ 15
 | S.S Career Academy answered |
Let money with Ken = x. Then, money with Mac = x + £ 3.
Now, 3x = (x + x + £ 3) + £ 2
x = £ 5.
Therefore Total money with Mac and Ken = 2x + £ 3 = £ 13.
Now, 3x = (x + x + £ 3) + £ 2
x = £ 5.Therefore Total money with Mac and Ken = 2x + £ 3 = £ 13.
A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?- a)2
- b)3
- c)6
- d)12
Correct answer is option 'C'. Can you explain this answer?
A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?
a)
2
b)
3
c)
6
d)
12
 | Akshita Joshi answered |
Given information:
- A is 3 years older than B.
- A is 3 years younger than C.
- B and D are twins.
To find: How many years older is C to D?
Let's analyze the given information step by step:
1. A is 3 years older than B:
- Let's assume B's age as x.
- Therefore, A's age will be x + 3 (as A is 3 years older than B).
2. A is 3 years younger than C:
- Let's assume C's age as y.
- Therefore, A's age will be y - 3 (as A is 3 years younger than C).
3. B and D are twins:
- This means B and D have the same age.
- Let's assume their age as z.
Now, we can equate the ages of A in both cases:
x + 3 = y - 3
Simplifying the equation, we get:
x - y = -6 ...(1)
Since B and D are twins, their ages are the same:
x = z ...(2)
To find the age difference between C and D, we need to find the difference between their ages:
C - D = y - z
Now, let's substitute the value of x from equation (2) into equation (1):
z - y = -6
Rearranging the equation, we get:
y - z = 6
Comparing this equation with C - D = y - z, we can conclude that C is 6 years older than D.
Therefore, the correct answer is option (c) 6.
- A is 3 years older than B.
- A is 3 years younger than C.
- B and D are twins.
To find: How many years older is C to D?
Let's analyze the given information step by step:
1. A is 3 years older than B:
- Let's assume B's age as x.
- Therefore, A's age will be x + 3 (as A is 3 years older than B).
2. A is 3 years younger than C:
- Let's assume C's age as y.
- Therefore, A's age will be y - 3 (as A is 3 years younger than C).
3. B and D are twins:
- This means B and D have the same age.
- Let's assume their age as z.
Now, we can equate the ages of A in both cases:
x + 3 = y - 3
Simplifying the equation, we get:
x - y = -6 ...(1)
Since B and D are twins, their ages are the same:
x = z ...(2)
To find the age difference between C and D, we need to find the difference between their ages:
C - D = y - z
Now, let's substitute the value of x from equation (2) into equation (1):
z - y = -6
Rearranging the equation, we get:
y - z = 6
Comparing this equation with C - D = y - z, we can conclude that C is 6 years older than D.
Therefore, the correct answer is option (c) 6.
A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether?- a)100
- b)104
- c)108
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether?
a)
100
b)
104
c)
108
d)
None of these
| | Rahul Mehta answered |
Since each pole at the corner of the plot is common to its two sides, so we have :
Total number of poles needed = 27 x 4 - 4 = 108 - 4 = 104.
A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes?- a)32 rolls
- b)54 rolls
- c)108 rolls
- d)120 rolls
Correct answer is option 'D'. Can you explain this answer?
A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes?
a)
32 rolls
b)
54 rolls
c)
108 rolls
d)
120 rolls
 | Lakshya Ias answered |
Number of cuts made to cut a roll into 10 pieces = 9.
Therefore Required number of rolls = (45 x 24)/9 = 120.
Therefore Required number of rolls = (45 x 24)/9 = 120.
The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner?- a)15
- b)29
- c)61
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner?
a)
15
b)
29
c)
61
d)
None of these
 | Abhay Malik answered |
Understanding the Tournament Structure
In a single-elimination tournament, each match results in one player losing and being eliminated from the competition. To determine a single winner from 30 players, we need to consider how many players must be eliminated.
Elimination Process
- In every match, one player loses and is out of the tournament.
- To find the overall winner, all players except one must be eliminated.
- Therefore, with 30 players, we need to eliminate 29 players.
Calculating Matches Played
- Since one player is eliminated per match, the number of matches played equals the number of players that need to be eliminated.
- Thus, to eliminate 29 players, 29 matches must be played.
Conclusion
- The minimum number of matches required to determine a winner among 30 players is 29.
- Therefore, the correct answer is option B (29).
This simple structure ensures that the tournament can proceed efficiently, with each match progressively narrowing down the competitors until only one remains.
In a single-elimination tournament, each match results in one player losing and being eliminated from the competition. To determine a single winner from 30 players, we need to consider how many players must be eliminated.
Elimination Process
- In every match, one player loses and is out of the tournament.
- To find the overall winner, all players except one must be eliminated.
- Therefore, with 30 players, we need to eliminate 29 players.
Calculating Matches Played
- Since one player is eliminated per match, the number of matches played equals the number of players that need to be eliminated.
- Thus, to eliminate 29 players, 29 matches must be played.
Conclusion
- The minimum number of matches required to determine a winner among 30 players is 29.
- Therefore, the correct answer is option B (29).
This simple structure ensures that the tournament can proceed efficiently, with each match progressively narrowing down the competitors until only one remains.
A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?- a)28
- b)29
- c)31
- d)35
Correct answer is option 'A'. Can you explain this answer?
A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?
a)
28
b)
29
c)
31
d)
35
 | Academic Studio answered |
Clearly, we have :
A = B - 3 ...(i)
D + 5 = E ...(ii)
A+C = 2E ...(iii)
B + D = A+C = 2E ...(iv)
A+B + C + D + E = 150 ...(v)
From (iii), (iv) and (v), we get: 5E = 150 or E = 30.
Putting E = 30 in (ii), we get: D = 25.
Putting E = 30 and D = 25 in (iv), we get: B = 35.
Putting B = 35 in (i), we get: A = 32.
Putting A = 32 and E = 30 in (iii), we get: C = 28.
A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle?- a)4
- b)8
- c)12
- d)24
Correct answer is option 'D'. Can you explain this answer?
A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle?
a)
4
b)
8
c)
12
d)
24
 | Ias Masters answered |
Total number of routes from Bristol to Carlisle = (4 x 3 x 2) = 24.
In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?- a)6
- b)12
- c)18
- d)24
Correct answer is option 'B'. Can you explain this answer?
In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?
a)
6
b)
12
c)
18
d)
24
 | EduRev UPSC answered |
Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x (4/3) = 24.
If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.
Therefore Number of girls in the class = (36 - 24) = 12.
If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.
Therefore Number of girls in the class = (36 - 24) = 12.
There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?- a)20
- b)30
- c)50
- d)60
Correct answer is option 'D'. Can you explain this answer?
There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?
a)
20
b)
30
c)
50
d)
60
| | Gayatri Basak answered |
**Problem Solving:**
To solve this problem, we can use a system of linear equations. Let's assume that the number of deer is represented by 'x' and the number of peacocks is represented by 'y'.
**Step 1: Formulate the Equations:**
We are given two pieces of information:
1. The total number of heads is 80.
2. The total number of legs is 200.
From these two pieces of information, we can form two equations:
Equation 1: x + y = 80 (since the total number of heads is 80)
Equation 2: 4x + 2y = 200 (since each deer has 4 legs and each peacock has 2 legs)
**Step 2: Solve the Equations:**
To solve the system of equations, we can use the method of substitution or elimination. In this case, let's solve it using the method of substitution.
From Equation 1, we can express x in terms of y: x = 80 - y
Substituting this value of x into Equation 2, we get:
4(80 - y) + 2y = 200
Simplifying the equation, we have:
320 - 4y + 2y = 200
Combining like terms, we get:
-2y = 200 - 320
-2y = -120
Dividing both sides by -2, we get:
y = 60
**Step 3: Find the Number of Peacocks:**
From our solution, we found that y = 60, which represents the number of peacocks.
Therefore, the correct answer is option D) 60.
To solve this problem, we can use a system of linear equations. Let's assume that the number of deer is represented by 'x' and the number of peacocks is represented by 'y'.
**Step 1: Formulate the Equations:**
We are given two pieces of information:
1. The total number of heads is 80.
2. The total number of legs is 200.
From these two pieces of information, we can form two equations:
Equation 1: x + y = 80 (since the total number of heads is 80)
Equation 2: 4x + 2y = 200 (since each deer has 4 legs and each peacock has 2 legs)
**Step 2: Solve the Equations:**
To solve the system of equations, we can use the method of substitution or elimination. In this case, let's solve it using the method of substitution.
From Equation 1, we can express x in terms of y: x = 80 - y
Substituting this value of x into Equation 2, we get:
4(80 - y) + 2y = 200
Simplifying the equation, we have:
320 - 4y + 2y = 200
Combining like terms, we get:
-2y = 200 - 320
-2y = -120
Dividing both sides by -2, we get:
y = 60
**Step 3: Find the Number of Peacocks:**
From our solution, we found that y = 60, which represents the number of peacocks.
Therefore, the correct answer is option D) 60.
Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start?- a)7 times
- b)8 times
- c)9 times
- d)11 times
Correct answer is option 'B'. Can you explain this answer?
Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start?
a)
7 times
b)
8 times
c)
9 times
d)
11 times
| | Baishali Chavan answered |
Let's analyze the problem step by step.
Step 1: Find the LCM of the time intervals
The time intervals given are 6, 5, 7, 10, and 12 seconds. To find the least common multiple (LCM) of these intervals, we can list their multiples and find the smallest number that appears in each list.
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 7: 7, 14, 21, 28, 35, ...
Multiples of 10: 10, 20, 30, ...
Multiples of 12: 12, 24, 36, ...
From the lists, we can see that the smallest number that appears in each list is 30. Therefore, the LCM of the time intervals is 30 seconds.
Step 2: Calculate the number of times they toll together in one hour
In one hour, there are 60 minutes * 60 seconds = 3600 seconds.
To find the number of times the bells toll together, we need to divide the total time (3600 seconds) by the LCM of the time intervals (30 seconds).
3600 seconds / 30 seconds = 120
This means that the bells toll together 120 times in one hour.
However, we need to exclude the one at the start. Therefore, the correct answer is 120 - 1 = 119 times.
So, the correct option is b) 8 times.
Step 1: Find the LCM of the time intervals
The time intervals given are 6, 5, 7, 10, and 12 seconds. To find the least common multiple (LCM) of these intervals, we can list their multiples and find the smallest number that appears in each list.
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 7: 7, 14, 21, 28, 35, ...
Multiples of 10: 10, 20, 30, ...
Multiples of 12: 12, 24, 36, ...
From the lists, we can see that the smallest number that appears in each list is 30. Therefore, the LCM of the time intervals is 30 seconds.
Step 2: Calculate the number of times they toll together in one hour
In one hour, there are 60 minutes * 60 seconds = 3600 seconds.
To find the number of times the bells toll together, we need to divide the total time (3600 seconds) by the LCM of the time intervals (30 seconds).
3600 seconds / 30 seconds = 120
This means that the bells toll together 120 times in one hour.
However, we need to exclude the one at the start. Therefore, the correct answer is 120 - 1 = 119 times.
So, the correct option is b) 8 times.
Mr. Johnson was to earn £ 300 and a free holiday for seven weeks' work. He worked for only 4 weeks and earned £ 30 and a free holiday. What was the value of the holiday?- a)£ 300
- b)£ 330
- c)£ 360
- d)£ 420
Correct answer is option 'B'. Can you explain this answer?
Mr. Johnson was to earn £ 300 and a free holiday for seven weeks' work. He worked for only 4 weeks and earned £ 30 and a free holiday. What was the value of the holiday?
a)
£ 300
b)
£ 330
c)
£ 360
d)
£ 420
 | Nishanth Rane answered |
$50,000 per year, but due to a promotion, he will now earn $65,000 per year.
A bird shooter was askgd how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?- a)9
- b)18
- c)27
- d)36
Correct answer is option 'A'. Can you explain this answer?
A bird shooter was askgd how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?
a)
9
b)
18
c)
27
d)
36
| | Rhea Reddy answered |
There were all sparrows but six' means that six birds were not sparrows but only pigeons and ducks.
Similarly, number of sparrows + number of ducks = 6 and number of sparrows + number of pigeons = 6.
This is possible when there are 3 sparrows, 3 pigeons and 3 ducks i.e. 9 birds in all.
What is the smallest number of ducks that could swim in this formation - two ducks in front of a duck, two ducks behind a duck and a duck between two ducks?- a)3
- b)5
- c)7
- d)9
Correct answer is option 'A'. Can you explain this answer?
What is the smallest number of ducks that could swim in this formation - two ducks in front of a duck, two ducks behind a duck and a duck between two ducks?
a)
3
b)
5
c)
7
d)
9
| | Roshni Sarkar answered |
Explanation:
Formation Description:
- Two ducks in front of a duck
- Two ducks behind a duck
- A duck between two ducks
Minimum Number of Ducks:
- In this formation, we need at least 3 ducks to satisfy all the given conditions:
1. Duck 1: Two ducks in front
2. Duck 2: A duck between two ducks
3. Duck 3: Two ducks behind
Therefore, the smallest number of ducks that could swim in this formation is 3, which is option 'A'.
Formation Description:
- Two ducks in front of a duck
- Two ducks behind a duck
- A duck between two ducks
Minimum Number of Ducks:
- In this formation, we need at least 3 ducks to satisfy all the given conditions:
1. Duck 1: Two ducks in front
2. Duck 2: A duck between two ducks
3. Duck 3: Two ducks behind
Therefore, the smallest number of ducks that could swim in this formation is 3, which is option 'A'.
A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is- a)12
- b)15
- c)18
- d)20
Correct answer is option 'B'. Can you explain this answer?
A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is
a)
12
b)
15
c)
18
d)
20
 | Shreya Das answered |
Given Information:
- Father is now 3 times as old as his son.
- 5 years back, father was 4 times as old as his son.
Let the age of the son be x years.
Calculating Father's age:
- Father's age = 3x (as per the first statement)
Calculating Son's age 5 years ago:
- Son's age 5 years ago = x - 5
Calculating Father's age 5 years ago:
- Father's age 5 years ago = 3x - 5
Using the second statement:
- 3x - 5 = 4(x - 5)
- 3x - 5 = 4x - 20
- x = 15
Therefore, the age of the son is 15 years (option B).
- Father is now 3 times as old as his son.
- 5 years back, father was 4 times as old as his son.
Let the age of the son be x years.
Calculating Father's age:
- Father's age = 3x (as per the first statement)
Calculating Son's age 5 years ago:
- Son's age 5 years ago = x - 5
Calculating Father's age 5 years ago:
- Father's age 5 years ago = 3x - 5
Using the second statement:
- 3x - 5 = 4(x - 5)
- 3x - 5 = 4x - 20
- x = 15
Therefore, the age of the son is 15 years (option B).
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