Real Numbers: Numerical Word Problems Quiz

Explanation
The correct answer is 1*1/2. To solve this problem, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is Rs. 800, the annual interest rate is 10%, and interest is compounded semiannually (n=2). We need to find the value of t. By plugging in the given values into the formula and solving for t, we find that t is equal to 1/2. Therefore, it will take 1/2 year for the sum to become Rs. 926.10.

Explanation
Kamal defeats Bimal by 5 seconds in a 100m race. To find the speed of Bimal, we need to calculate the time taken by Bimal to complete the race. Since the distance is the same for both Kamal and Bimal, we can use the formula speed = distance/time. Given that Kamal's speed is 18 kmph, we can calculate the time taken by Kamal to complete the race as 100m/18 kmph = 5.56 seconds. Since Bimal takes 5 seconds longer than Kamal, his time would be 5.56 + 5 = 10.56 seconds. Using the formula speed = distance/time, we can calculate the speed of Bimal as 100m/10.56 seconds = 9.47 m/s or 9.47 * 3.6 kmph = 34.09 kmph, which is approximately equal to 14.4 kmph.

Explanation
The length of the train is given as 240 meters. The man is walking in the opposite direction of the train at a speed of 3 kmph. In 10 seconds, the train crosses the man.

To find the speed of the train, we need to convert the time and speed to the same unit. Since the length of the train is given in meters, we convert the speed of the man from kmph to m/s.

3 kmph = 3 * (1000/3600) m/s = 5/6 m/s

Now, we can use the formula speed = distance/time. The distance is the length of the train, which is 240 meters, and the time is 10 seconds.

speed = 240/10 = 24 m/s

Finally, we convert the speed from m/s to kmph.

24 m/s = 24 * (3600/1000) kmph = 86.4 kmph

Therefore, the speed of the train is 86.4 kmph.

Explanation
To find the speed of the stream, we need to calculate the speed of the boat in still water. The boatman rows 1 km in 5 minutes along the stream, which means his speed is 1 km/5 min = 12 kmph. Similarly, he rows 6 km in 1 hour against the stream, which means his speed is 6 kmph. The speed of the stream can be found by taking the difference between the speed of the boat in still water and the speed against the stream: 12 kmph - 6 kmph = 6 kmph. Therefore, the speed of the stream is 6 kmph.

Explanation
A can complete 1/3 of the work in 5 days, which means A can complete the entire work in 15 days. B can complete 2/5 of the work in 10 days, so B can complete the entire work in 25 days. When A and B work together, their combined efficiency is 1/15 + 1/25 = 8/75 of the work per day. Therefore, it will take them 75/8 = 9.375 days to complete the work. Rounded to the nearest whole number, the answer is 10.

Explanation
If 7 men can complete a piece of work in 12 days, it means that the total work requires 7 men * 12 days = 84 man-days. To complete double the work, it would require 2 * 84 man-days = 168 man-days. Since the time has been reduced to 8 days, the additional men required can be calculated as 168 man-days / 8 days = 21 men. Therefore, 21 additional men will be required to complete double the work in 8 days.

Explanation
The slower pipe fills the tank at a rate that is three times slower than the faster pipe. Let's assume that the faster pipe takes x minutes to fill the tank. Therefore, the slower pipe will take 3x minutes to fill the tank.

When both pipes work together, they can fill the tank in 36 minutes. This means that in one minute, they fill 1/36th of the tank.

Since the faster pipe fills the tank in x minutes, it fills 1/x of the tank in one minute. Similarly, the slower pipe fills 1/3x of the tank in one minute.

Adding these rates together, we get 1/x + 1/3x = 1/36.

Combining like terms and solving for x, we find that x = 54 minutes.

Therefore, the slower pipe alone will take 3x = 3 * 54 = 162 minutes to fill the tank, which is equal to 2 hours 42 minutes.

Explanation
Since the student scores 4 marks for every correct answer and loses 1 mark for every wrong answer, we can set up the equation 4x - (200 - x) = 200, where x is the number of questions answered correctly. Simplifying this equation, we get 5x - 200 = 200, which further simplifies to 5x = 400. Dividing both sides by 5, we find that x = 80. Therefore, the student answered 80 questions correctly.

Explanation
The average of odd numbers up to 100 is 50 because there are 50 odd numbers from 1 to 100. The sum of these odd numbers is 2500 (1+3+5+...+99). To find the average, we divide the sum by the number of terms, which is 50. Therefore, 2500 divided by 50 is 50, making the average 50.

Explanation
A's income is 25% less than B's income, which means A's income is 75% of B's income. To find out how much B's income is more than A's, we need to calculate the difference between B's income and A's income as a percentage of A's income.
Let's assume B's income is 100 units. A's income would be 75 units (75% of B's income).
The difference between B's income and A's income is 25 units.
To find out the percentage, we divide the difference (25 units) by A's income (75 units) and multiply by 100.
Therefore, B's income is 33 1/3% more than A's income.