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At what time, between 4 and 5 o'clock, will the minute and hour hands be together?
To calculate the time when the minute and hour hands are together between 4 and 5 o'clock, we need to consider the relative speeds of the two hands.
The minute hand moves at a rate of 6 degrees per minute, while the hour hand moves at a rate of 0.5 degrees per minute (since it covers 30 degrees in 60 minutes).
Let's denote the time when the minute and hour hands are together as "x" minutes past 4 o'clock.
The minute hand will cover x minutes at a rate of 6 degrees per minute, resulting in an angular displacement of 6x degrees.
The hour hand will cover x minutes at a rate of 0.5 degrees per minute, resulting in an angular displacement of 0.5x degrees.
To find the time when the minute and hour hands are together, we need to solve the equation:
6x = 0.5x + 120
x = (120/5.5) = (240/11) minutes = 21 (9/11) minutes
Therefore, the minute and hour hands are together at 4 hours, 21 minutes, and 9/11 minutes past 4 o'clock.
A watch gains 7 seconds in 4 minutes and is correctly set at 10:00 AM. What time will it show at 11:00 PM on the same day?
It is given that the watch gains 7 seconds in 4 minutes => 105 seconds in 60 minutes (1hr). From 10:00 AM to 11:00 PM on the same day, the time is 13 hours.
In 13 hours, the watch will gain (105*13) = 1365 seconds => 22 minutes 45 seconds. Therefore, the watch will show 11:22:45 PM
The correct option is B.
In the question below, a statement is given, followed by two courses of action numbered I and II. A course of action is a practicable and feasible step or administrative decision for follow-up, improvement or further action concerning the problem, policy, etc. Based on the information in the statement, you have to assume everything in the statement to be true and decide which of the suggested courses of action logically follow(s) to pursue.
Statement: The pollution levels in a city have reached hazardous levels, posing significant risks to the health and well-being of its residents.
Course of Action I: Implement strict emission control regulations and standards for industries and vehicles to reduce pollution levels.
Course of Action II: Promote and incentivize the use of public transportation and carpooling to decrease the number of vehicles on the road.
Both courses of action can be considered as feasible steps to address the high pollution levels in the city.
Course of Action I focuses on implementing strict emission control regulations and standards for industries and vehicles. By imposing stricter regulations, such as limiting emissions and enforcing rigorous inspections, the city can effectively reduce pollution levels. This course of action aims to hold industries and vehicle owners accountable for their emissions and encourages the adoption of cleaner technologies, ultimately leading to a decrease in pollution.
Course of Action II suggests promoting and incentivizing the use of public transportation and carpooling. By encouraging residents to utilize public transportation systems and carpooling services, the number of vehicles on the road can be significantly reduced. This would subsequently decrease the overall emissions and pollution generated by individual vehicles. Providing incentives, such as discounted fares, dedicated carpool lanes, and improved public transportation infrastructure, can encourage more people to opt for sustainable modes of transportation.
Implementing both of these courses of action in conjunction can lead to a comprehensive approach to address the pollution problem. Course of Action I focuses on reducing emissions at the source, while Course of Action II aims to decrease the overall number of vehicles contributing to pollution. By combining these strategies, the city can make significant strides in mitigating pollution levels and improving the environmental quality for its residents.
Today is Saturday. After 243 days, it will be:
Since each day repeats after 7 days, which implies we need to check the number of odd days.
Rem (243/7) = 5.
Therefore, After 243 days, it will be (Saturday +5) = Thursday.
The correct option is D
P said, "Q likes cricket."
Q said, "I don't like cricket."
R said, "P is lying."
If only one person tells the truth, who are the liars?
Assume P tells the truth, which implies Q and R are the liars.
Assume Q tells the truth, which implies P is a liar and R is the truth-teller. (This is not possible since it is given that only one person tells the truth.)
Assume R tells the truth, which implies P is a liar and Q is telling the truth. (This is not possible since it is given that only one person tells the truth.)
Hence, Q and R are the liars.
The correct option is B.
What is the angle between the minute and hour hands of the clock at 8:40 PM?
At 8:00 PM, the hour hand is at 240 degrees from vertical (12 o'clock).
In 40 minutes, the hour hand will move 40*(0.5) = 20 degrees ( since the hour hand moves at 0.5 degrees per minute). The hour hand made an angle (240+20) = 260 degrees from the vertical.
In 40 minutes, the minute hand will move 40*(6) = 240 degrees from the vertical. ( since the minute hand moves at 6 degrees per minute)
Hence, the angle between the hand is (260-240) = 20 degrees.
The correct option is C.
If the angle between 2 hands of a clock is 35 degrees and the hour hand is between 3 and 4, what time does the clock show?
The hour hand covers 30 degrees in 1 hour or 0.5 degrees / min
The min hand covers 360 degrees in 1 hour of 6 degrees/ min
Hence, we can say that the the minute hand gains 6 - 0.5 = 5.5 degrees on hour hand, every minute.
At 3 p.m. the angle between the hands was 90 degrees
Hence there can be two possible cases, the minute hand can form a angle of 35 degrees both before and after the it crosses the hour hand.
Let x be the number of minutes past 3.
case 1
90 - 5.5x = 35
x = 10
case 2
5.5x - 90 = 35
x = 125/5.5 = 250/11 = 22 8/11
Hence the angle between hour hand and minute hand will be 35 degrees at 10 and 22 8/11 minutes past 3
Below each question are given two statements I and II. These statements may be either independent causes or may be effects of independent causes or a common cause. One of these statements may be the effect of the other statement. Read both the statements and decide which of the following answer choice correctly depicts the relationship between these two statements.
I: The electricity bills for households have increased.
II: The government raised the tariffs for electricity consumption by 10%.
In this scenario, it can be inferred that the increase in electricity bills for households (Statement I) is caused by the government raising the tariffs for electricity consumption by 10% (Statement II). When the government increases the tariffs, the cost of electricity per unit consumed by households goes up. As a result, the electricity providers charge higher rates to the consumers, leading to an increase in electricity bills.
Thus, Statement I (increase in electricity bills) is the effect, and Statement II (government raising the tariffs) is the cause of this effect. Therefore, the correct answer is Option B.
In the question below, a statement is given, followed by two courses of action numbered I and II. A course of action is a practicable and feasible step or administrative decision for follow-up, improvement or further action concerning the problem, policy, etc. Based on the information in the statement, you have to assume everything in the statement to be true and decide which of the suggested courses of action logically follow(s).
Situation: A multinational corporation is experiencing low employee engagement and high turnover rates among its senior executives.
Option 1: Offer financial incentives and salary raises to senior executives to improve job satisfaction and retention.
Option 2: Implement a comprehensive leadership development program to nurture and enhance the skills of senior executives.
While financial incentives may provide short-term motivation, they are not always effective in addressing deeper employee engagement and turnover issues. Relying solely on financial incentives may create a culture of short-term motivation rather than long-term commitment. It is essential to focus on developing leadership skills and creating a supportive work environment to address the underlying causes of low engagement and high turnover.
By implementing a leadership development program, the organization invests in its senior executives' growth and professional development. This program can include training, mentoring, and coaching sessions to strengthen their leadership abilities, enhance engagement, and improve job satisfaction. Developing effective leaders can positively impact employee engagement and reduce turnover rates.
By choosing Option 2, the organization recognizes the importance of investing in leadership development as a long-term solution to enhance employee engagement and reduce turnover rates among senior executives.
In the question below, a statement is given, followed by two courses of action numbered I and II. A course of action is a practicable and feasible step or administrative decision for follow-up, improvement or further action concerning the problem, policy, etc. Based on the information in the statement, you have to assume everything in the statement to be true and decide which of the suggested courses of action logically follow(s) to pursue.
Statement: The crime rate in a city has increased drastically, causing fear and insecurity among residents.
Course of Action I: Increase the presence of police patrols in high-crime areas and implement stricter law enforcement measures.
Course of Action II: Launch community outreach programs and initiatives to promote crime prevention and create a sense of unity and responsibility among residents.
Both courses of action can be considered as feasible steps to address the problem of increased crime rate in the city. Course of Action I focuses on immediate law enforcement measures to deter criminals and maintain public safety. By increasing police presence and implementing stricter measures, potential criminals may be deterred from committing crimes, leading to a decrease in the crime rate. Course of Action II, on the other hand, aims to address the root causes of crime by fostering community engagement and building stronger relationships between residents and law enforcement agencies. This approach can contribute to preventing crime through proactive measures such as education, awareness campaigns, and community cooperation. Implementing both courses of action in conjunction could lead to a comprehensive strategy for combating crime and ensuring the safety and well-being of the city's residents.
It has been 25 days since Sofu first met her friend, Kitto. Kitto had promised to meet her today, but when Sofu called, he said they could only meet on a Wednesday, 10 days from now. On which day of the week did they first meet?
To determine the day of the week when Sofu and Kitto finally met, we need to calculate the total number of days between their initial meeting and the day they were supposed to meet.
Sofu met Kitto 25 days ago. Let's denote this day as Day 1.
Kitto informed Sofu that they would meet after 10 days from today, which is a Wednesday. Let's denote this day as Day 2.
To find the day of the week when they finally met, we need to add the number of days between Day 1 and Day 2 and determine the resulting day of the week.
The number of days between Day 1 and Day 2 is calculated as follows:
25 days + 10 days = 35 days.
Since there are 7 days in a week, we divide 35 by 7 to determine the remainder.
35 days ÷ 7 = 5 weeks with no remainder.
This means that after 5 weeks, the day of the week will remain the same.
Since Day 1 was a Wednesday, and 5 weeks have passed, the day of the week when Sofu and Kitto finally met is also a Wednesday.
Therefore, they met on a Wednesday.
Question: In a village, there are three types of people: Knights, Knaves, and Jokers. Knights always tell the truth, Knaves always lie, and Jokers can either tell the truth or lie. You encounter three villagers, A, B, and C. Each of them belongs to one of the three types. They make the following statements:
A: "B is a Knight."
B: "C is a Knave."
C: "A and B are of the same type."
Determine the types of A, B, and C.
Let's assume A is a knight, which implies A always tells the truth, implying B is a knight, which is not possible ( SInce only one knight is there).
Now if A is a knave, which implies B is surely not Knight, which implies B is a joker => C is the knight ( which is impossible since C's statement is definitely false.)
Therefore, A must be a joker, which implies C is a knave and B is a knight.
The correct option is D.
At what time, between 3 and 4 o'clock, will the hands of a clock be together?
When the time of the clock is 3 o'clock, the hour hand is at 3, and the minute hand is at 12, making an angle of 90 degrees. We know that the relative velocity of the minute hand w.r.t the hour hand is 5.5 degrees per minute.
Hence, it will take (90/5.5) minutes to make the angle between the hands 0 degrees.(the hands will be together)
(90/5.5)= (180/11) minutes past 3. => $$16\frac{4}{11}$$ minutes past 3.
The correct option is C.
Find the time shown by the clock if the hour hand is between 8 and 9 and the minute hand is pointing in the exact opposite direction of the hour hand.
The hour hand covers 30 degrees in 1 hour or 0.5 degrees / min
The min hand covers 360 degrees in 1 hour of 6 degrees/ min
Hence, we can say that the the minute hand gains 6 - 0.5 = 5.5 degrees on hour hand, every minute.
At 8 pm the the hour hand will be ahead of minute hand by 30*8 = 240 degrees.
Hence, the minute hand will have to cover 60 degrees more w.r.t the hour hand for them to point in opposite direction/ for the angle between them to be 180 degrees.
let x be the number of minutes taken by the minute hand to do the same.
5.5x = 60
x = 60/5.5 = 120/11 = 10 10/11
Ram places three identical cones of radius on a table in such a way that each cone base touches the other two, also the altitude of the cone is perpendicular to the table. The radius
of the circle drawn through the cone vertices would be?
The top view of the three cones can be seen in the figure below.
The three centres will form an equilateral triangle. R= 2/3*$$\sqrt{3 }$$r
R= 2/$$\sqrt{3 }$$*r
R is larger than r.
Option C
Three lamps A, B and C as shown in the figure above are burning using oil as its source of energy. Three incense sticks, E, F and G are taken. E is dipped in oil, F is dipped in petrol and G is dipped in water and are immediately placed over the wick of A, B and C respectively. Then
Oil and water will put off the flame while petrol will increase the flame.
Option B
Ramu has several friends and all of them are well settled in India. $$\frac{1}{5^{th}}$$ of Ramu's friends went to Mumbai and $$\frac{1}{3^{rd}}$$ of his friends went to Delhi, three times the difference of these two went to Chennai and only one went to Pune. How many of his friends went to Mumbai?
Let the total number of friends be T
The total number of friends went to Chennai= 3 (T/3-T/5)= 2T/5
Number of friends went to Pune= T-T/5-2T/5-T/3
= T-14T/15
=T/15=1
T=15
The number of friends who went to Mumbai=T/5 =15/5=3
Which of the below pendulums will move the slowest, if each one of them is displaced by an angle of $$60^\circ$$ from the center?
The time period of a pendulum(T) =2$$ \pi \sqrt{\frac{l}{g} }$$.
The time period is directly proportional to the length of the pendulum.
More the time period, lesser will be the speed of the pendulum.
So Option B is correct.
A fast train leaves Chennai to Bengaluru and at the same point in time a slow train leaves from Bengaluru to Chennai. The fast train moves at a speed of 60 km /hr and the slow train moves at half of the speed of the fast train. Both these trains meet at a point after some time. Which of these trains are further away from Chennai when they meet? (Do not consider the length of the train)
The moment they will meet they will be equidistant from the two cities.
Option C is correct.
Read the following information answer the question that follow:
Some people enter a conference room and get seated around a circular table.
The following is known about them.
(i) The first to enter sits opposite to one who belongs to Durgapur but right of Ranchi.
(ii) Teacher belongs to Kolkata and is right to IT professional.
(iii) The guy from Durgapur is adjacent to teacher and architect and opposite to doctor.
(iv) The guy from Ranchi is opposite to architect who is not from Dharbhanga.
(v) The doctor belongs to Chennai and sits adjacent to those who came at 3rd and 6th positions.
(vi) The guy from Burdwan is adjacent to guys who came at 3rd and 5th positions.
(vii) Professor who didn’t come at 5th position is equidistant from guys from Ranchi and Durgapur.
The dancer is from-
From the given figure we can see that dancer is from Ranchi
Many people argue that the death penalty deters murder. However, the notorious killer Tom Hanks deliberately moved to a state that imposes the death penalty just before embarking on a series of ferocious murders. Thus, it seems clear that the existence of the death penalty does not serve as a deterrent to murder. The argument above may best be characterized as:
Premise:
1. people argue that the death penalty prevents murder.
2. notorious killer Tom Hanks deliberately moved to a state that imposes the death penalty just before embarking on a series of ferocious murders.
Argument: "the existence of the death penalty does not serve as a deterrent to murder"
The argument is drawn on a specific example, hence, Option C is correct.
Four children A, B, C and D are having some chocolates each.
A gives B as many as he already has, he gives C twice of what C already has and he gives D thrice of what D already has.
Now, D gives (1/8)th of his own chocolates to B.
Then A gives 10% chocolates he now owns to C and 20% to B.
Finally, all of them have 35 chocolates each. What is the original number of chocolates each had in the beginning?
Let A, B, C, D have a, b, c, d chocolates respectively initially.
D gets thrice as many as he already has from A which makes a total of 4d chocolates with D.
He gives one-eigth of that to B which leaves D with 3.5d Chocolates.
Now 3.5 d = 35 => d = 10
Now, A has given b, 2c, 3d chocolates to B, C, D respectively at first which left him with (a-b-2c-3d) chocolates.
Then he gave 10% of the remaining chocolates to C and 20% to B.
He finally has 0.7(a-b-2c-3d) chocolates.
0.7(a-b-2c-3d) = 35
=>(a-b-2c-3d) = 50 = k (say)
C got 2c chocolates at first and then again 10% of 'k' from A.
C finally has 3c + 0.1k = 35
=> c = 10
B got b chocolates at first and then again 20% of 'k' from A and 0.5d from D.
B finally has 2b + 0.5d + 0.2k = 35
=> b = 10
For A, 0.7(a-b-2c-3d) = 35
=> a = 110
Ramaswami was studying for his examinations and the lights went off. It was around 1:00 a.m. He lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last six hours and the thin one two hours less. When he finally
went to sleep, the thick candle was twice as long as the thin one. For how long did Ramaswami study in candle light?
Assume that the initial lenght of both the candle was L and Vipul studied for X hours.
In X hours, total thick candle burnt = XL/6
In X hours, total thin candle burnt = XL/4
After X hours, total thick candle remaining = L - XL/6
After X hours, total thin candle remaining = L - XL/4
Also, it is given that the thick candle was twice as long as the thin one when he finally went to sleep.
(L - XL/6) = 2(L - XL/4)
(6 - X)/6 = (4 - X)/2
(6 - X) = 3*(4 - X)
6 - X = 12 - 3X
2X = 6
X = 3
The numerator and denominator of a fraction is in the ratio 2:3. If 6 are subtracted from the numerator the value of the fraction becomes $$\frac{2}{3}$$ of the original fraction. The numerator of the original fraction is,
Let the numerator be 2x and the denominator be 3x. On subtracting 6 from the numerator, we get the equation as:
On solving this, we get x = 9 and the numerator as 18.
A person wanted to withdraw X rupees and Y paise from the bank. But cashier made a mistake and gave him Y rupees and X paise. Neither the person nor the cashier noticed that. After spending 20 paise, the person counts the money. To his surprise, he has double the amount he wanted to withdraw.
Find X and Y. (1 Rupee = 100 Paise)
Expressing the money he wanted to withdraw in terms of paise: 100x + y
Expressing the amount the cashier gave him: 100y + x
After spending 20paise from the withdrawn money, he finds he still has double the amt, he actually wished to withdraw.
So the eqn is: (100y+x) - 20 = 2(100x+y)
=> 98y - 199x = 20 ...(1)
Only option B satisfies eqn 1 among the given options.
A drawer contains 10 black and 10 brown socks which are all mixed up. What is the fewest number of socks you can take from the drawer without looking and be sure to get a pair of the same color?
For this, we have to consider the worst possible case.
Suppose we get a black piece in the 1st pick and then a brown one in the 2nd pick.
In the 3rd pick, we will either get a black one or a brown one and when it will be placed with the previous two pieces, we will definitely get a pair of socks of the same colour.
If for a particular value of the variable x, the following holds good, $$17 = \frac{17x}{(1 - x)}$$, then compute the value of (2x)*x.
Solving the eqn:
we get x = (1/2)
So 2 x (1/2) x (1/2) = 1/2
In a certain language, (A) 'Sun shines brightly' is written as 'ba lo sul'; (B) ' Houses are brightly lit' is written as 'kado udo ari ba'; and (C) 'Light comes from sun' as 'dapi kup lo nro'. What words will be written for 'sun' and 'brightly'?
In statements A and B, 'brightly' is the only common word used and in their interpretation, 'ba' is the only common word used. So, 'brightly' corresponds to 'ba'.
In statements A and C, 'sun' is the only common word used and in their interpretation, 'lo' is the only common word used. So, 'sun' corresponds to 'lo'.
Beautiful beaches attract people, no doubt about that. Just look at the city’s most beautiful beaches, which are amongst the most overcrowded places in the state. Which of the following exhibits a pattern of reasoning similar to the one exhibited in the argument above?
The example given in the question starts with a strong argument, which is followed by a strong reasoning- city’s most beautiful beaches, are amongst the most overcrowded places in the state.
In option A, the reasoning given is not so strong as appearing at the same drinking hole doesn't guarantee both of them drinking at the same time.
In option B, an argument is made and then another argument is made by negating the given argument. hence, eliminated.
In option C, a strong argument is made and which is supported by the reasoning given by observations like the one given in the question.
In option D, the conclusion that the users of Tally software have more time for other activities just because of more efficient software seems to be weak, as it is not mentioned that the workload remains same.
Hence, option C is the best option exhibiting a similar reasoning as given in the question.
Steel cylinders are made so that each one has a large and small hole through the middle. In the drawing six cylinders have been stacked on top of each other. To stop the cylinders from rolling on the smooth floor they are wedged by heavy blocks at each side of bottom row. If the heavy blocks are removed what would be the position of the cylinder when they stopped rolling?
Given all the cylinders have a larger hole and a smaller hole, the centre of mass of the cylinders will be somewhere shifted towards the one with smaller hole. When left to role, the cylinder will come to rest such that the centre of mass is at the lowest possible height wrt the ground due to gravity. Only Option C shows the possible final position of the cylinders.
A man has a job which requires him to work 8 straight days and rest on the ninth day. If he started work on a Monday, the 12th time he rests will be on what day of the week?
For the man to take $$12^{th}$$ time rest he has to work for $$\left(12\times\ 8\right)=96$$ days and have rest for 11 days
Total days lapsed will be 96+11 = 107 and hence the $$12^{th}$$ rest day is $$108^{th}$$ day.
Day 1 is monday. After this Day 8 will be Monday. In general $$\left(7k+1\right)^{th}$$ day is Monday
Therefore $$106^{th}$$ day is Monday. $$108^{th}$$ day or $$12^{th}$$ rest day will be Wednesday
Jaideep was given some money by his mother on his birthday. Jaideep spent all of it in five
stores. In each store he spent one rupee more than half of what he had when he came in.
How much did he get from his mother?
Let $$y_i\ $$ represent the money Jaideep has when he enters the shop i.
Money spent by him = $$\frac{\ y_i}{2}+1\ $$ and money remaining withhim is$$\frac{\ y_i}{2}-1\ $$
For 5th shop it is given that $$\frac{\ y_5}{2}-1\ =0\ $$ hence $$y_5$$ = 2. Therefore amount remaining with him after he exists Shop 4 is Rs 2
Which can be tabulated as
Hence $$\frac{\ y_4}{2}-1\ $$ = 2 or $$y_4$$ = 6
Similarly $$y_1$$, $$y_2$$and$$y_3$$ can be calculated and the table gets filled as follows
Hence he got Rs 62 from his mother
Sonal, a mathematician defines a number as 'connected by 6' if it is divisible by 6, or if the sum of digits is 6, or if 6 is one of the digits of the number.Other numbers are 'not connected by 6'. As per the definition, the number of integers, from 1-60 (both inclusive) which are not connected with 6 is
For the number to be connected to 6 it has to be either
(i) Divisible by 6 which are : 6,12,18,24,30,36,42,48,54,60
(ii) Has 6 as their digits which are : 6,16,26,36,46,56,60
(iii) Sum of digit has to be 6 which are : 6,15,24,33,42,51,60
Here we see that 6,24,36,42,60 are repeated. Overall there are 17 numbers that are connected to 6. Thus 60-17 = 43 is the required answer
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