Analytics Fte Drive - 2019

Explanation
A and B can do a piece of work in 45 days and 40 days respectively, which means that in one day they can complete 1/45th and 1/40th of the work respectively. They began to do the work together, so in one day they can complete (1/45 + 1/40) of the work. Let's assume they worked together for x days before A left. So, the work done by A and B together in x days is (x/45 + x/40). The remaining work is completed by B alone in 23 days, so B can complete the remaining work in 1/23rd of the work per day. Setting up the equation (x/45 + x/40) + 23(1/40) = 1, we can solve for x which gives x = 9. Therefore, A left the work after 9 days.

Explanation
The given information states that the sum of money is to be distributed among A, B, C, and D in the proportion of 5:2:4:3. This means that for every 5 parts A gets, B gets 2 parts, C gets 4 parts, and D gets 3 parts.

The question also states that C gets Rs.1000 more than D. This means that the difference between C's share and D's share is Rs.1000.

Since the total proportion is 5+2+4+3 = 14 parts, we can calculate the value of 1 part by dividing the total sum of money by 14.

Let's assume that 1 part is equal to x.

So, C's share would be 4x and D's share would be 3x.

According to the given information, C's share is Rs.1000 more than D's share.

Therefore, 4x - 3x = Rs.1000

Simplifying this equation, we get x = Rs.1000.

Now, we can calculate B's share, which is 2x.

So, B's share is 2 * Rs.1000 = Rs.2000.

Hence, the correct answer is Rs.2000.

Explanation
The external benefactor gives three times the teacher's contribution, so the total amount contributed by the teachers and the benefactor is four times the teacher's contribution. If the teachers offer to pay 50% more than the students, their contribution would be 1.5 times the student's contribution. Therefore, the equation can be set up as 1.5x + 3x = 4200, where x is the student's contribution. Solving this equation, we find that x = 600. Therefore, the teacher's contribution would be 1.5 * 600 = 900.

Explanation
Since the ratio of A's and B's monthly incomes is 4:5, let's assume A's monthly income to be 4x and B's monthly income to be 5x.

Similarly, the ratio of A's and B's expenses is 5:6. Let's assume A's monthly expenses to be 5y and B's monthly expenses to be 6y.

We are given that A saves Rs.25 per month, so A's monthly income minus expenses equals 25.
Therefore, 4x - 5y = 25.

We are also given that B saves Rs.50 per month, so B's monthly income minus expenses equals 50.
Therefore, 5x - 6y = 50.

Solving these two equations simultaneously, we find that x = 40 and y = 35.

Substituting these values back, we get A's monthly income as 4x = 4 * 40 = Rs. 160 and B's monthly income as 5x = 5 * 40 = Rs. 200.

Therefore, the correct answer is Rs. 400 and Rs. 500.

Explanation
The batsman scored 110 runs, out of which 3 boundaries and 8 sixes contributed to 6 runs each (3x6 = 18) and 48 runs respectively (8x6 = 48). Therefore, the total runs scored by boundaries and sixes is 18 + 48 = 66. To find the percentage of runs made by running between the wickets, we subtract the runs made by boundaries and sixes from the total score: 110 - 66 = 44. The percentage can be calculated by dividing the runs made by running (44) by the total score (110) and multiplying by 100: (44/110) x 100 = 40%. However, this is not one of the options given, so we need to convert it into a mixed fraction: 40% = 40/100 = 4/10 = 2/5. Converting it into a mixed fraction gives us 2/5 = 4/10 = 4/10 = 1/2. Therefore, the batsman made 45 5/11% of his total score by running between the wickets.

Explanation
From the given information, we can set up two equations: 8 = 0.04a and 4 = 0.08b. Solving these equations, we find that a = 200 and b = 50. Then, we can calculate c by dividing b by a, which gives us c = 50/200 = 1/4. Therefore, the value of c is 1/4.

Explanation
If the price of petrol increases by 25%, the user would need to cut down their consumption by 20% in order to keep their expenditure on petrol constant. This is because a 25% increase in price would result in a 20% decrease in consumption to maintain the same overall expenditure.

Explanation
To find the ratio in which the teas should be mixed, we can set up an equation based on the given information. Let the quantity of tea costing Rs. 192 per kg be x kg and the quantity of tea costing Rs. 150 per kg be y kg.

The cost price of the mixed tea is (192x + 150y) and the selling price is (194.40 * (x + y)).

Given that the profit percentage is 20%, we can write the equation as:
194.40 * (x + y) - (192x + 150y) = 0.2 * (192x + 150y)

Simplifying the equation, we get:
1.44x = 0.94y

Dividing both sides by y, we get:
x/y = 0.94/1.44

Simplifying further, we find:
x/y = 47/72

Therefore, the ratio in which the teas should be mixed is 47:72, which can be approximated to 2:5.

Explanation
When the selling price is doubled, the profit triples. This means that the profit is directly proportional to the selling price. Let's assume the original selling price is S and the original profit is P. When the selling price is doubled, it becomes 2S. According to the given information, the profit also triples, so it becomes 3P. Therefore, the ratio of the new profit to the original profit is 3P/P = 3. To convert this ratio to a percentage, we multiply by 100. So, the profit percent is 3 * 100 = 300%. However, the question asks for the profit percent, not the increase in profit percent. Therefore, the correct answer is 100%.

Explanation
A and B invest in the business in the ratio 3:2, which means that for every 3 parts invested by A, B invests 2 parts. This implies that the total investment is divided into 5 parts.

Since A's share is Rs. 855, we can calculate the value of one part of the investment by dividing A's share by 3: 855 / 3 = Rs. 285.

Now, we know that A's share is 3 parts, so the total profit can be calculated by multiplying the value of one part by the total number of parts: 285 * 5 = Rs. 1425.

However, 5% of the total profit goes to charity, so the actual profit is 95% of Rs. 1425, which is Rs. 1425 * 0.95 = Rs. 1353.75.

Therefore, the correct answer is Rs. 1500.

Explanation
Since there were 60 people participating in the auction and everyone bought at least one T-shirt, it means that there were a total of 60 T-shirts sold. If 42 Reds United T-shirts and 30 Blues T-shirts were sold, it means that there were a total of 72 T-shirts sold. However, since no one bought more than one T-shirt of the same type, it means that there must be an overlap between the number of Reds United T-shirts and Blues T-shirts sold. Therefore, the number of people who bought both T-shirts can be calculated by subtracting the total number of T-shirts sold from the sum of Reds United T-shirts and Blues T-shirts sold: 72 - 60 = 12. Therefore, the answer is 12.

Explanation
The probability of picking a red marble on the first draw is 6/13, since there are 6 red marbles out of a total of 13 marbles. After the first marble is drawn, there are now 12 marbles left, with 5 of them being red. Therefore, the probability of picking a red marble on the second draw is 5/12. To find the probability of both events happening, we multiply the probabilities together: (6/13) * (5/12) = 30/156 = 5/26.

Explanation
Let's assume Aman's present age is x. After 20 years, his age will be x + 20. And 10 years back, his age was x - 10. According to the given condition, x + 20 = 10(x - 10). Solving this equation, we get x = 13.3 years.

Explanation
Ten years ago, let the age of the son be x. Therefore, the age of the mother would be 3x. After ten years, the son's age would be x+10 and the mother's age would be 3x+10. According to the given information, 3x+10 = 2(x+10). Solving this equation, we get x = 10. Therefore, the present age of the son is 10 and the present age of the mother is 3(10) = 30. The ratio of their present ages is 30:10, which simplifies to 3:1. Simplifying further, we get the ratio as 7:3.

Explanation
To form a committee with at least 3 men, we can consider two cases: selecting 3 men and 2 women, or selecting 4 men and 1 woman.

For the first case, there are C(7,3) ways to choose 3 men from the 7 available, and C(6,2) ways to choose 2 women from the 6 available. Therefore, the number of ways to select 3 men and 2 women is C(7,3) * C(6,2).

For the second case, there are C(7,4) ways to choose 4 men from the 7 available, and C(6,1) ways to choose 1 woman from the 6 available. Therefore, the number of ways to select 4 men and 1 woman is C(7,4) * C(6,1).

Adding these two cases together gives us the total number of ways to form the committee: C(7,3) * C(6,2) + C(7,4) * C(6,1) = 756.

Explanation
The respective ratio of the expenditures of Companies X and Y in 2000 is 15:22. This can be determined by using the given information that the incomes of the two companies in 2000 were in the ratio of 3:4. Since profit is calculated as income minus expenditure, we can assume that the percentage profit earned by both companies in 2000 is the same. Therefore, the ratio of their expenditures can be calculated by dividing the ratio of their incomes by the assumed common profit percentage, which results in 15:22.

Explanation
The percentage profit earned by Company Y in 1997 can be calculated using the formula %Profit = (Income - Expenditure) x 100. We are given that the expenditure of Company Y in 1997 was Rs. 220 crores. Let's assume that the percentage profit earned by Company Y in 1997 is p%. Using the formula, we can write the equation as p% = (Income - 220) x 100. We need to find the income in 1997, which is represented by the variable "Income". To solve for Income, we can rearrange the equation as Income = (p% / 100) + 220. Since the answer is given as Rs. 297 crores, it means that p% is equal to 77%. Substituting this value into the equation, we get Income = (77 / 100) + 220 = 297 crores. Therefore, the income in 1997 was Rs. 297 crores.

Explanation
In order to find the total profit of the two companies together in 1996, we need to subtract the expenditure from the income. Since the expenditures of Company X and Y in 1996 were equal and the total income of the two companies in 1996 was Rs. 342 crores, we can assume that each company had an income of Rs. 171 crores. Therefore, the total profit of the two companies together in 1996 would be Rs. 171 crores - Rs. 171 crores = Rs. 102 crores.

Explanation
Based on the given information, we know that C and N are diagonally opposite to each other. Since N is sitting in the second line facing North, and C is sitting in the first line facing South, N must be sitting third to the right of O. Therefore, the correct answer is N.

Explanation
If B shifts to the place of E, E shifts to the place of Q, and Q shifts to the place of B, then Q will be opposite to D. Since P is opposite to D and Q is now opposite to P, the person second to the left of Q will be the person opposite to O. Therefore, the answer is Q.

Explanation
Based on the given information, we can determine the seating arrangement as follows:

M - O - E - D - B
N - Q - P - C - A

From this arrangement, we can see that A and M are diagonally opposite to each other. Therefore, the correct answer is AM.

Explanation
In 1997, the total number of candidates qualified from all the states together is 720. In 1998, the total number of candidates qualified from all the states together is 980. To find the percentage, we divide the number of candidates qualified in 1997 by the number of candidates qualified in 1998 and multiply by 100. (720/980) * 100 = 73.47%. Rounding to the nearest whole number, the percentage is approximately 73%. Therefore, the given answer of 80% is incorrect.

Explanation
The average candidates who appeared from State Q during the given years can be calculated by finding the sum of the number of candidates who appeared from State Q in each year and dividing it by the number of years. In this case, the sum of the number of candidates who appeared from State Q in each year is 8100 + 9500 + 8700 + 9700 + 8950 = 44950. Since there are 5 years, the average is 44950/5 = 8990.

Explanation
In the year 2001, the number of candidates appeared from State P has the maximum percentage of qualified candidates. This can be determined by comparing the number of qualified candidates in each year for State P and calculating the percentage of qualified candidates for each year. Among the given years, 2001 has the highest percentage of qualified candidates for State P.

Explanation
To determine if a number can be the square of a natural number, we need to check if it is a perfect square. A perfect square is a number that can be expressed as the product of two equal natural numbers. By finding the square root of each given number, we can determine if it is a perfect square. The square root of 30976 is 176, the square root of 75625 is 275, the square root of 28561 is 169. However, the square root of 143642 is not a whole number, indicating that it cannot be the square of a natural number.

Explanation
To find the speed in km/hr, we need to convert the distance from meters to kilometers and the time from minutes to hours. The cyclist covers a distance of 750m in 2 minutes and 30 seconds, which is equivalent to 2.5 minutes. Converting the distance to kilometers, we divide 750m by 1000 to get 0.75km. Converting the time to hours, we divide 2.5 minutes by 60 to get 0.0417 hours. Finally, we divide the distance by the time to get the speed, which is 0.75km/0.0417hr = 18 km/hr.

Explanation
The pattern in the series is that it alternates between adding 3 and subtracting 2. Starting with 7, we add 3 to get 10, then subtract 2 to get 8, then add 3 to get 11, and so on. Following this pattern, the next number should be obtained by subtracting 2 from the previous number, which gives us 10.

Explanation
The cost price of 100 oranges is Rs. 350. The selling price of 1 dozen (12) oranges is Rs. 48. Therefore, the selling price of 100 oranges is (48/12) * 100 = Rs. 400.

To calculate the profit or loss percentage, we use the formula:
Profit/Loss percentage = ((Selling Price - Cost Price) / Cost Price) * 100

In this case, the profit percentage is ((400 - 350) / 350) * 100 = 50/350 * 100 = 14 2/7%.

Therefore, the correct answer is "14 2/7% gain".

Explanation
The word 'DIRECTOR' has 8 letters. To find the number of words that can be formed using all the letters, we need to calculate the permutation of these letters. Since all the letters are different, the permutation can be calculated as 8 factorial, which is 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320. However, in this case, we need to divide by the factorial of the repeated letters. The letter 'R' appears twice, so we divide by 2 factorial (2!). Thus, the total number of words that can be formed is 40320 / 2 = 2160.

Explanation
The given answer, 9! / (2! * 2!), represents the number of ways the word SYNCHRONY can be rearranged. The word has 9 letters, but the letter "N" and the letter "Y" are repeated twice. Therefore, we need to divide the total number of arrangements (9!) by the number of arrangements of the repeated letters (2! * 2!). This ensures that we do not count the same arrangement multiple times.