Percentages And Time & Distance

Sid travels equal distances with speeds of 3 Km/hr, 4 Km/hr, and 5 Km/hr. The total time taken is 47 minutes. To find the total distance, we need to convert the time to hours. Since 1 hour is equal to 60 minutes, 47 minutes is equal to 47/60 hours. Let the distance be 'd'. According to the formula distance = speed × time, we can write the equation as d/3 + d/4 + d/5 = 47/60. By solving this equation, we can find the value of 'd' which is the total distance traveled by Sid.

Kabir traveled a total distance of 61 km in 9 hours. Let's assume he traveled x km on foot and (61-x) km on a bicycle. The time taken to travel on foot can be calculated by dividing the distance traveled on foot by the speed of walking, which is 4 km/hr. Similarly, the time taken to travel on a bicycle can be calculated by dividing the distance traveled on a bicycle by the speed of cycling, which is 9 km/hr. Since the total time taken is 9 hours, we can set up the equation x/4 + (61-x)/9 = 9. Solving this equation, we find that x = 16 km. Therefore, Kabir traveled 16 km on foot.

Let's assume the number is x. According to the given information, the difference between the number and two-fifths of the number is 510. Mathematically, this can be represented as x - (2/5)x = 510. Simplifying this equation gives us (3/5)x = 510. Dividing both sides by 3/5, we get x = 850. Therefore, 10% of the number (850) is 85.

Let's assume the values of A and B to be x and y respectively. The given equation can be written as (5/100)x + (4/100)y = (2/3)[(6/100)x + (8/100)y]. Simplifying this equation, we get 5x + 4y = (2/3)(6x + 8y). Expanding further, we get 5x + 4y = (4/3)x + (16/3)y. Rearranging the terms, we get (1/3)x = (8/3)y. Cross multiplying, we get 3x = 24y. Dividing both sides by 24, we get x/y = 8/3, which can be simplified to the ratio 4:3. Therefore, the ratio of A:B is 4:3.

Sheela traveled at a speed of 80 km/hr for 2 hours and 5 minutes, which is equivalent to 2.08 hours. The distance covered during this time is calculated by multiplying the speed by the time, giving us 80 km/hr * 2.08 hr = 166.4 km. Subtracting this distance from the total distance of 350 km, we get 350 km - 166.4 km = 183.6 km. Sheela then traveled the remaining distance of 183.6 km at a speed of 60 km/hr. To calculate the time taken for this, we divide the distance by the speed, resulting in 183.6 km / 60 km/hr = 3.06 hours. Adding this time to the initial time of 5:20 AM, we get 5:20 AM + 3.06 hr = 8:26 AM. Therefore, Sheela reached city A at 8:26 AM. However, none of the given options match this time, so the correct answer is not available.

The average speed is calculated by dividing the total distance by the total time taken. In this case, Shawn drives 200 km at 40 km/hr, which takes him 5 hours. On the return trip, he drives the same distance of 200 km at 20 km/hr, which takes him 10 hours. The total distance covered is 400 km and the total time taken is 15 hours. Therefore, the average speed is 400 km/15 hours = 26.67 km/hr.

Since Vicky takes 5 hours in total for both going and coming back, we can assume that he spends 2.5 hours each way. We can use the formula: distance = speed * time. So, for the first trip, the distance would be 3 Km/hr * 2.5 hours = 7.5 Km. For the return trip, the distance would be 2 Km/hr * 2.5 hours = 5 Km. Thus, the total distance between his house and school is 7.5 Km + 5 Km = 12.5 Km. However, since he is traveling back and forth, we need to divide this distance by 2, resulting in a distance of 6 Km.

Let's assume the number as x. According to the given information, when 35 is subtracted from x, it becomes 80% of x. So, we can write the equation as x - 35 = 0.8x. By solving this equation, we find that x = 175. Now, we need to find four-fifth of this number, which is (4/5) * 175 = 140. Therefore, the correct answer is 140.

The second number is 12% of the first number. This can be calculated by dividing the second number (12) by the first number (100) and multiplying by 100 to get the percentage. 12/100 * 100 = 12%.

In this question, let the first number be x and the second number be y. According to the given information, when 25% of x is subtracted from y, y reduces to five-sixth of itself. Mathematically, this can be represented as y - 0.25x = (5/6)y. Simplifying this equation, we get 0.25x = (1/6)y. Dividing both sides of the equation by y, we get (0.25x)/y = 1/6. Simplifying further, we get x/y = 2/3. Therefore, the ratio of the first number to the second number is 2:3.

If the smaller number is 20 and the difference of two numbers is 20% of the larger number, we can set up the equation: Larger number - Smaller number = 0.2 * Larger number. Simplifying this equation, we get: 0.8 * Larger number = Smaller number. Plugging in the value of the smaller number as 20, we have: 0.8 * Larger number = 20. Solving for the larger number, we find that it is 25.

If one number is 80% of the other, we can set up the equation x = 0.8y, where x is the smaller number and y is the larger number. Additionally, we are given that 4 times the sum of their squares is 656, so we can write the equation 4(x^2 + y^2) = 656. Substituting x = 0.8y into the second equation, we get 4(0.64y^2 + y^2) = 656. Simplifying this equation, we find that 4.56y^2 = 656, which means y^2 = 143.86. Taking the square root of both sides, we find that y ≈ 11.99. Since y must be a whole number, the closest whole number to 11.99 is 12. Substituting y = 12 into the equation x = 0.8y, we find that x = 0.8(12) = 9.6. Since x must also be a whole number, the closest whole number to 9.6 is 10. Therefore, the numbers are 8 and 10.

The winning candidate received 11628 votes out of the total votes cast. To find the percentage, we divide the winning candidate's votes by the total votes and multiply by 100. So, (11628/20000) * 100 = 58.14%. Rounded to the nearest whole number, the winning candidate received 57% of the total votes.

In order to find the percentage of the total who failed, we need to calculate the percentage of boys who failed and the percentage of girls who failed. Since 42% of the boys passed, 58% of the boys failed. Similarly, since 30% of the girls passed, 70% of the girls failed. Now, we need to find the weighted average of the percentage of boys who failed and the percentage of girls who failed. Since there are 1100 boys and 700 girls, the weightage of boys is 1100/(1100+700) = 11/18 and the weightage of girls is 700/(1100+700) = 7/18. Calculating the weighted average, we get (11/18)(58%) + (7/18)(70%) = 62 2/3%. Therefore, the percentage of the total who failed is 62 2/3%.

Let's assume the total number of students in the school is x. We are given that 20% of students are below 8 years of age, so the number of students below 8 years is 0.2x.
We are also given that the number of students above 8 years of age is 2/3 of the number of students of 8 years of age, which is 48. So, the number of students above 8 years is (2/3)*48 = 32.
Therefore, the total number of students in the school is the sum of students below 8 years and students above 8 years: 0.2x + 32.
We know that the total number of students in the school is 100, so we can set up the equation: 0.2x + 32 = 100.
Simplifying the equation, we get 0.2x = 68.
Dividing both sides by 0.2, we get x = 340.
Therefore, the total number of students in the school is 340.

The given information states that x% of y is equal to 100, and y% of z is equal to 200. To find the relationship between x and z, we can analyze the second statement. If y% of z is 200, it implies that z is twice the value of y. Since x% of y is 100, it means that y is equal to x. Therefore, z must be equal to 2x, which is the correct relationship between x and z.

Let's assume the total number of workers in the office is x. From the given information, we know that 72% prefer tea, which is 0.72x, and 44% prefer coffee, which is 0.44x. Since each worker prefers either tea or coffee, the total number of workers who prefer tea or coffee is 0.72x + 0.44x. However, we have counted the 40 workers who like both tea and coffee twice, so we need to subtract 40 from the total. Therefore, the equation becomes 0.72x + 0.44x - 40 = x. Solving this equation, we find that x = 250, which is the total number of workers in the office.

To find the percentage, we need to divide the given amount (Rs. 1987.50) by the total amount (Rs. 2650) and then multiply by 100. Therefore, (1987.50/2650) * 100 = 75%. This means that Rs. 1987.50 is 75% of Rs. 2650.

Dora rides her bicycle for a total distance of 10 km + 12 km = 22 km. The first 10 km is covered at a speed of 12 km/hr, which takes 10 km / 12 km/hr = 5/6 hr. The remaining 12 km is covered at a speed of 10 km/hr, which takes 12 km / 10 km/hr = 6/5 hr. The total time taken for the trip is 5/6 hr + 6/5 hr = 61/30 hr. The average speed for the entire trip is the total distance (22 km) divided by the total time (61/30 hr), which is approximately 10.8 km/hr.

The speeds of Ram, Lakshman, and Bharat are in the ratio 4:3:5. This means that for every 4 units of distance Ram travels, Lakshman travels 3 units, and Bharat travels 5 units. Since they are all walking from place P to place Q, the time ratio to reach Q will be the inverse of their speed ratio. Therefore, the time ratio will be 1/4:1/3:1/5, which simplifies to 15:20:12.

To find out if 60% of 264 is the same as 15% of 1056, we can calculate both values. 60% of 264 is (60/100) * 264 = 158.4. Similarly, 15% of 1056 is (15/100) * 1056 = 158.4. Therefore, both values are equal, indicating that 60% of 264 is the same as 15% of 1056.

If Varun travels at 10 kmph, he will reach point A at 12 noon, which means it will take him 2 hours to reach there. If he travels at 15 kmph, he will reach point A at 2 PM, which means it will take him 4 hours to reach there. To reach point A at 1 PM, he needs to travel for 3 hours. Therefore, he must travel at a speed of 12 kmph to reach point A at 1 PM.

If 15% of 40 is greater than 25% of a number by 2, then we can set up the equation (15/100) * 40 = (25/100) * x + 2. Simplifying this equation, we get 6 = (25/100) * x + 2. Subtracting 2 from both sides, we have 4 = (25/100) * x. Multiplying both sides by 100/25, we get 16 = x. Therefore, the number is 16.

The statement "None of these" is the correct answer because the relationship between A and B cannot be determined based on the given information. The question only provides the equations A = x% of y and B = y% of x, but it does not specify any values for x and y. Therefore, it is impossible to determine whether A is smaller than B, greater than B, or if it depends on the relative sizes of x and y.

In this question, we are given that 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. We are also given that 4275 eligible candidates belonged to other categories.
Let's assume the total number of applicants is x.
Since 5% of the applicants were found ineligible, the number of eligible candidates is 95% of x, which is 0.95x.
Since 85% of the eligible candidates belonged to the general category, the number of eligible candidates belonging to other categories is 15% of 0.95x, which is 0.15 * 0.95x = 0.1425x.
We are given that 0.1425x = 4275. Solving this equation, we find x = 30000. Therefore, the number of candidates who applied for the examination is 30,000.

Dishu travels a distance of 250 miles from A to B in 5 1/2 hours, which means his average speed is 250 miles divided by 5.5 hours, resulting in 45.45 mph. On his return journey from B to A, he takes 4 hours and 30 minutes, which is equivalent to 4.5 hours. The average speed for this journey is 250 miles divided by 4.5 hours, resulting in 55.56 mph. To find the overall average speed, we can take the harmonic mean of the two speeds: (2 * 45.45 * 55.56) / (45.45 + 55.56) = 50 mph.

Ricky is twice as fast as John, which means Ricky can cover the same distance in half the time it takes John. Similarly, John is thrice as fast as Paul, so John can cover the same distance in one-third of the time it takes Paul. Therefore, if Paul takes 54 minutes to cover the journey, John will take one-third of that time, which is 18 minutes.

The question states that 5 out of 2250 parts of the Earth is Sulphur. To find the percentage of Sulphur in Earth, we need to divide the number of Sulphur parts (5) by the total number of parts (2250) and then multiply by 100. This calculation gives us (5/2250) * 100 = 0.22%. However, none of the given answer choices match this calculation. Therefore, the correct answer is not available.

The cost to copy the first 1000 sheets is Rs. 1000. For the remaining 4000 sheets, a 2% discount is applied. The discount is 2/100 * 4000 * 1 = Rs. 80. Therefore, the total cost for copying 5000 sheets is Rs. 1000 + Rs. 80 = Rs. 1080.

The agent receives a commission of 2.5% on the sales of cloth. If he earns Rs.12.50 as commission, we can set up the equation 2.5% of x = 12.50, where x represents the worth of the cloth sold. To solve for x, we divide both sides of the equation by 2.5% (or 0.025), giving us x = 12.50 / 0.025 = 500. Therefore, the cloth sold through him on that day is worth 500 rupees.

If 20% of a is equal to b, then b% of 20 would be the same as 4% of a. This is because if 20% of a equals b, then b% of 20 would be b/100 * 20, which is equal to 4/100 * a, or 4% of a.

Rohan is walking at a speed of 5 km/hr. In 5 minutes, he crosses the bridge. To find the length of the bridge, we need to convert the time from minutes to hours. Since there are 60 minutes in an hour, 5 minutes is equal to 5/60 = 1/12 hours. Distance = Speed x Time, so the length of the bridge is 5/12 x 5 = 25/12 km. To convert this to meters, we multiply by 1000, giving us 25000/12 meters. Simplifying this, we get 1250 meters, which matches the given answer.

Rahul covers one-half of the distance in two-thirds of the total time, which means he covers 3 km in 30 minutes. This implies that his speed is 6 km/hr. Since he has 15 minutes left to cover the remaining 3 km, his speed must be the same, which is 6 km/hr. Therefore, the correct answer is 12 km/hr.

Saksham performs 3/5 of the total journey by rail, 17/20 by bus, and the remaining 6.5 km on foot. Since the distances traveled by rail, bus, and foot are given as fractions, we need to find a common denominator to compare them. The common denominator for 5 and 20 is 20. So, 3/5 can be written as 12/20 and 17/20 remains the same. Adding these fractions together, we get 12/20 + 17/20 = 29/20. This means that Saksham has traveled a total distance of 29/20 of the journey. To find the actual distance, we need to multiply 29/20 by the distance he traveled on foot, which is 6.5 km. Multiplying these, we get (29/20) * 6.5 = 9.35 km. Therefore, the total journey is 9.35 km, which is closest to 65 km.

Let's assume that Y is paid Rs. X per week. According to the information given, X is paid 120% of Y's salary. This can be represented as X = 1.2Y. The total amount paid to both X and Y is Rs. 550. Therefore, we can write the equation X + Y = 550. Substituting the value of X from the first equation into the second equation, we get 1.2Y + Y = 550. Simplifying this equation, we find that Y = 250. Therefore, Y is paid Rs. 250 per week.

Rishi travels at a speed of 40 kmph from P to Q and returns by increasing his speed by 50%. To find the average speed for both trips, we can use the formula: Average speed = (2 * Speed1 * Speed2) / (Speed1 + Speed2). Plugging in the values, we get (2 * 40 * 60) / (40 + 60) = 4800 / 100 = 48 kmph. Therefore, the average speed for both trips is 48 kmph.

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Let Aditya's speed be x kmph.
According to the given information, Abhishek takes 2 hours more than Aditya to cover 30 km, so Abhishek's speed is 30/(x-2) kmph.
If Abhishek doubles his speed, his new speed would be 2*(30/(x-2)) kmph.
According to the second statement, Abhishek would take 1 hour less than Aditya, so the equation becomes 30/x - 1 = 2*(30/(x-2)).
Simplifying this equation, we get x = 10.
So, Abhishek's speed is 30/(x-2) = 30/(10-2) = 5 kmph.

Jaya takes 20% more time than Asha to reach her home. Since both Jaya and Asha travel at the same speed of 40 kmph, the time taken by Jaya would be 20% more than Asha's time. This means Jaya takes 1.2 times the time taken by Asha.
Let's calculate Asha's time first. Asha's house is at a distance of 30 km from the office, and she is traveling at a speed of 40 kmph. So, her time taken would be 30 km / 40 kmph = 0.75 hours.
Now, let's calculate Jaya's time. Jaya takes 1.2 times Asha's time, which is 1.2 * 0.75 hours = 0.9 hours.
Since Jaya is also traveling at a speed of 40 kmph, we can calculate the distance of Jaya's house by multiplying her time by her speed: 0.9 hours * 40 kmph = 36 km.
Therefore, the distance of Jaya's house from the office is 36 km.

If James' income increased by 10% and his tax rate increased to 15%, his net income would increase by Rs.350. This means that the increase in income after tax is equal to Rs.350. We can set up an equation to solve for James' income. Let's assume his initial income is x. After increasing by 10%, his new income is 1.1x. After applying the tax rate of 15%, his net income is 0.85(1.1x) = 0.935x. The increase in net income is 0.935x - x = 0.935x - 1x = -0.065x = Rs.350. Solving for x, we find that x = Rs.350 / -0.065 ≈ Rs. 10,000. Therefore, James' income is Rs. 10,000.

The total cost of the items George bought is Rs. 25. Out of this, 30 paise (0.30 Rs) went towards sales tax on taxable purchases. The tax rate is given as 6%. To find the cost of the tax-free items, we need to subtract the tax amount from the total cost.

Let x be the cost of the tax-free items.

Therefore, x + 0.30 = 25

Simplifying the equation, we get x = 24.70

So, the cost of the tax-free items is Rs. 24.70, which is closest to Rs. 19.70.

The average percent increase of population per year can be calculated by finding the total increase in population over the given time period and dividing it by the number of years. In this case, the total increase in population is 2,62,500 - 1,75,000 = 87,500. Since the time period is a decade, which is 10 years, the average percent increase per year is 87,500/10 = 8,750. To find the percentage, we divide this value by the initial population (1,75,000) and multiply by 100. This gives us (8,750/1,75,000) * 100 = 5%. Therefore, the correct answer is 5%.

Let's assume Micky's monthly income is x. According to the given information, Jerry's monthly income is 20% less than Micky's, so Jerry's monthly income is (0.8x). Tom's monthly income is 30% more than Jerry's, so Tom's monthly income is (1.3 * 0.8x). The difference between Tom and Micky's monthly incomes is Rs. 800, so we can set up the equation (1.3 * 0.8x) - x = 800. Solving this equation, we find that x = 16,000. Therefore, Jerry's monthly income is 0.8 * 16,000 = Rs. 16,000.

The value of '?' can be found by calculating the sum of 88% of 370 and 24% of 210 and then subtracting it from 118. This can be represented as (0.88 * 370) + (0.24 * 210) - ? = 118. Simplifying the equation, we get (325.6 + 50.4) - ? = 118. Combining like terms, we have 376 - ? = 118. Solving for '?', we subtract 118 from both sides, resulting in ? = 258.

To find out how much faster Vishal must travel to make the trip in 5/6 hour less time, we need to calculate the average speed. Vishal traveled 50 km in 2 hours and 30 minutes, which is equal to 2.5 hours. Therefore, his average speed is 50 km / 2.5 hours = 20 km/hr. To make the trip in 5/6 hour less time, he needs to reduce his travel time by 5/6 hour. So, his new travel time will be 2.5 hours - 5/6 hour = 2 hours. To find out how much faster he must travel, we divide the distance (50 km) by the new travel time (2 hours), which gives us 25 km/hr. Therefore, Vishal must travel 10 km/hr faster on average to make the trip in 5/6 hour less time.

Karan travels the first half of the journey at a speed of 21 km/hr and the second half at a speed of 24 km/hr. Since the time taken for both halves is the same, we can assume that the distance covered in each half is equal. Let's say the distance of each half is 'x' km.

Therefore, the time taken for the first half is x/21 hours and the time taken for the second half is x/24 hours.

Since the total time taken for the journey is 10 hours, we can write the equation as x/21 + x/24 = 10.

By solving this equation, we find that x = 112 km.

Hence, the total journey is 2x, which is equal to 2 * 112 = 224 km.

The average speed for the first 320 km of the tour can be calculated by finding the total distance traveled and dividing it by the total time taken. In this case, Sam traveled 160 km at a speed of 64 km/hr, which took 2.5 hours (160/64). He then traveled another 160 km at a speed of 80 km/hr, which took 2 hours (160/80). Therefore, the total distance traveled is 320 km and the total time taken is 4.5 hours (2.5 + 2). Dividing the total distance by the total time gives an average speed of 71.11 km/hr.

Katrina takes three times as many steps as Priyanka in a given time. If Priyanka counts 75 steps, then Katrina would take 3 times that amount, which is 225 steps. However, Katrina only counts 150 steps, which means that the escalator is moving in the opposite direction of Katrina's movement. Therefore, the total number of steps on the escalator is the sum of the steps counted by Katrina and Priyanka, which is 150 + 75 = 225 steps. Since the escalator is moving downwards, the number of visible steps is equal to the total number of steps minus the steps taken by Priyanka, which is 225 - 75 = 150 steps. However, the question specifically asks for the number of visible steps, so the correct answer is 120.

The first number is 200% greater than the second number because when any number is divided by 12, the dividend becomes 1/4th of the other number. In this case, the second number is 1/4th of the first number, so the first number is four times greater than the second number. Four times greater is equivalent to 400%, but since the question asks for the percentage by which the first number is greater than the second number, we subtract 100% to get 300%.