Alligation Or Mixture: Quantitative Aptitude Trivia Test!

Explanation
To find the amount of sugar to be mixed, we can use the concept of weighted averages. Let's assume x kilograms of sugar costing Rs. 6.10 per kg is mixed with 126 kg of sugar costing Rs. 2.85 per kg.

The cost of the mixture is given by (6.10x + 2.85 * 126) / (x + 126).

We want to gain 20% by selling the mixture at Rs. 4.80 per kg. So, the selling price of the mixture is 1.2 times the cost price, which is 1.2 * (6.10x + 2.85 * 126) / (x + 126).

According to the question, this selling price is Rs. 4.80 per kg.

Simplifying the equation, we get: (1.2 * (6.10x + 2.85 * 126)) / (x + 126) = 4.80.

Solving this equation, we find that x is approximately equal to 69 g.

Explanation
To find the ratio in which the person must mix the three kinds of wheat, we can set up an equation based on the cost per kg of each type of wheat. Let the ratio be x:y:z.

According to the given information, the cost per kg of the first kind of wheat is Rs. 1.20, the second kind is Rs. 1.44, and the third kind is Rs. 1.74. The mixture is worth Rs. 1.41 per kg.

So, we can set up the equation:

(1.20x + 1.44y + 1.74z) / (x + y + z) = 1.41

Simplifying this equation, we get:

1.20x + 1.44y + 1.74z = 1.41x + 1.41y + 1.41z

0.21x + 0.03y + 0.33z = 0

To solve this equation, we can choose any two variables and assume a value for one of them. Let's assume x = 11.

So, the ratio becomes 11:y:z. Substituting this into the equation, we get:

0.21(11) + 0.03y + 0.33z = 0

2.31 + 0.03y + 0.33z = 0

0.03y + 0.33z = -2.31

Now, we can try different values for y and z that satisfy this equation. By trial and error, we find that y = 77 and z = 7 satisfy the equation.

Therefore, the ratio in which the person must mix the three kinds of wheat is 11:77:7.

Explanation
The man traveled a distance of 80 km in 7 hours. Let's assume he traveled x km on foot and (80 - x) km on a bicycle. The time taken to travel x km on foot at a rate of 8 km per hour would be x/8 hours. Similarly, the time taken to travel (80 - x) km on a bicycle at a rate of 16 km per hour would be (80 - x)/16 hours. According to the given information, the total time taken is 7 hours. Therefore, we can form the equation x/8 + (80 - x)/16 = 7. Solving this equation, we get x = 32 km. Hence, the man traveled 32 km on foot.

Explanation
Each time 8 kg of milk is taken out and replaced with water, the amount of milk in the container decreases by 8 kg. After this process is repeated twice, the total amount of milk taken out and replaced with water is 8 kg + 8 kg = 16 kg. Therefore, the amount of milk remaining in the container is 80 kg - 16 kg = 64 kg.

Explanation
To achieve a mixture that is half water and half syrup, we need to remove some of the original mixture and replace it with water. Let's assume the total volume of the mixture is 8 units (3 parts water + 5 parts syrup).

If we remove 1 unit of the mixture, we will have 7 units left (3 parts water + 4 parts syrup). We then replace the 1 unit with water, making it 4 parts water + 4 parts syrup.

Now, the mixture is half water and half syrup, so the correct answer is 1/5, which represents the 1 unit that needs to be drawn off and replaced with water.

Explanation
Let's assume that the initial amount of liquid A in the can is 7x and the initial amount of liquid B is 5x. When 9 liters of the mixture is drawn off, the amount of liquid A becomes 7x - (7/12)*9 and the amount of liquid B becomes 5x - (5/12)*9. After the can is filled with liquid B, the amount of liquid A remains the same (7x - (7/12)*9) and the amount of liquid B becomes 5x - (5/12)*9 + 9. We are given that the ratio of A and B becomes 7:9, so we can set up the equation (7x - (7/12)*9) / (5x - (5/12)*9 + 9) = 7/9. Solving this equation, we find that x = 3. Therefore, the initial amount of liquid A in the can is 7x = 7*3 = 21 liters.

Explanation
To find the amount of sugar needed, we can use the concept of weighted averages. Let's assume that x kg of sugar costing Rs. 9 per kg is mixed with 27 kg of sugar costing Rs. 7 per kg. The total cost of the mixture is given by 9x + 7(27) and the total weight is x + 27.

We want a gain of 10% by selling the mixture at Rs. 9.24 per kg. This means the selling price should be 110% of the cost price. So, 1.1(9x + 7(27)) = 9.24(x + 27).

Solving this equation, we find x = 63 kg. Therefore, 63 kg of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg to achieve the desired gain.

Explanation
To find the ratio in which rice at Rs. 7.20 a kg should be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg, we can use the concept of weighted averages. Let the ratio be 2:3, meaning for every 2 kg of rice at Rs. 7.20, we mix it with 3 kg of rice at Rs. 5.70. The weighted average can be calculated as (2 * 7.20 + 3 * 5.70) / (2 + 3) = 6.30, which confirms that the mixture is worth Rs. 6.30 a kg. Therefore, the correct answer is 2:3.

Explanation
The price per kg of the mixed variety of rice can be calculated by finding the weighted average of the prices of Type 1 and Type 2 rice. Since the ratio of Type 1 to Type 2 rice is 2:3, we can assign weights of 2 and 3 respectively.

Using the weighted average formula, (2 * 15 + 3 * 20) / (2 + 3) = 90 / 5 = Rs. 18. Therefore, the price per kg of the mixed variety of rice is Rs. 18.

Explanation
Let's assume that the merchant sells x kg of sugar at 8% profit. This means that he sells (1000 - x) kg of sugar at 18% profit.

The profit earned from selling x kg at 8% is 0.08x.
The profit earned from selling (1000 - x) kg at 18% is 0.18(1000 - x).

Given that the merchant gains 14% on the whole, we can set up the equation:

0.08x + 0.18(1000 - x) = 0.14(1000)

Simplifying the equation, we get:

0.08x + 180 - 0.18x = 140

Combining like terms, we get:

-0.10x = -40

Dividing by -0.10, we find that x = 400.

Therefore, the quantity sold at 18% profit is 1000 - x = 1000 - 400 = 600 kg.

Explanation
In order to find the average weight of the whole class, we need to consider the total weight of all the students in both sections. Section A has 36 students with an average weight of 40kg, so the total weight of section A is 36 * 40 = 1440kg. Similarly, section B has 44 students with an average weight of 35kg, so the total weight of section B is 44 * 35 = 1540kg. Adding the total weights of both sections, we get 1440kg + 1540kg = 2980kg. Since the total number of students in the class is 36 + 44 = 80, the average weight of the whole class is 2980kg / 80 = 37.25kg.

Explanation
In order to find the batsman's average after the 17th inning, we need to determine his average before the 17th inning. Since he increased his average by 3 runs, we can subtract 3 from his average before the 17th inning to get his average after the 17th inning. Therefore, his average after the 17th inning is 39.

Explanation
The average expenditure of the eight people who spent Rs.12 each is (8 * 12) / 8 = Rs. 12. The ninth person spent Rs.8 more than the average, so their expenditure is Rs. 12 + Rs. 8 = Rs. 20. The total expenditure of all nine people is (8 * 12) + 20 = Rs. 96 + 20 = Rs. 116. However, the question asks for the total money spent, so we need to add the Rs. 8 that the ninth person spent more. Therefore, the total money spent is Rs. 116 + Rs. 8 = Rs. 117.

Explanation
To find the number of runs the player must make in his next innings, we need to consider the current average of runs and the desired increase in average. The average of 32 runs in 10 innings means the player has scored a total of 320 runs so far. To increase the average by 4, the total runs after the next innings should be (10+1) multiplied by the desired average, which is (10+1) multiplied by 36. This equals 396 runs. To find the number of runs needed in the next innings, we subtract the total runs scored so far (320) from the desired total runs (396), which gives us 76 runs. Therefore, the player must make 76 runs in his next innings.

Explanation
Let the original expenditure of the mess be Rs. X.
So, the average expenditure per head = X/35.
After the admission of 7 new students, the total number of students becomes 35+7=42.
The new average expenditure per head = (X+42)/42.
According to the given information, the new average expenditure per head is Re 1 less than the original average expenditure per head.
So, (X+42)/42 = X/35 - 1.
Simplifying this equation, we get X = Rs. 420. Therefore, the original expenditure of the mess was Rs. 420.

Explanation
The average of five consecutive odd numbers can be found by adding the numbers together and dividing by 5. In this case, the numbers given are (a+1), (a+2), (a+4), and (a+5). Adding these numbers together gives 4a + 12. Dividing by 5 gives (4a + 12)/5, which simplifies to (a+4). Therefore, the correct answer is (a+4).

Explanation
Three years ago, the average age of the family was 17 years. This means that the sum of the ages of the 5 family members three years ago was 17 x 5 = 85 years. Since then, a baby has been born and the average age of the family is still 17 years today. This means that the sum of the ages of the 6 family members today is also 17 x 6 = 102 years. Therefore, the age of the baby is 102 - 85 = 17 years. Since the baby was born three years ago, the present age of the baby is 17 - 3 = 14 years.

Explanation
The average speed for the whole journey can be found by taking the total distance traveled and dividing it by the total time taken. In this case, the motorist travels 150 km to the place and 150 km back, for a total distance of 300 km. The time taken for the first part of the journey is 150 km / 50 km per hour = 3 hours. The time taken for the return journey is 150 km / 30 km per hour = 5 hours. The total time taken for the whole journey is 3 hours + 5 hours = 8 hours. Therefore, the average speed is 300 km / 8 hours = 37.5 km per hour.

Explanation
The question is asking for the relationship between two numbers, where the average of the numbers is M and one of the numbers is N. The expression 2M - N represents the other number. This can be derived by multiplying the average (M) by 2 and subtracting the given number (N). Therefore, the correct answer is 2M - N.

Explanation
When one mango weighing 120 g is replaced by another, the average weight of the 9 mangoes increases by 20 g. This means that the total weight of the 9 mangoes increases by 20 g. Since the average weight of the 9 mangoes is the sum of their weights divided by 9, the total weight of the 9 mangoes is 9 times the average weight. Therefore, the weight of the new mango is 120 g - 20 g = 100 g.

Explanation
To solve this problem, we can set up an equation using the given information. Let's assume the number of wickets taken by the man before his last match is x. We know that his bowling average is 12.4, so the total runs he has conceded before the last match is 12.4x. After taking 5 wickets for 26 runs, his new average becomes 12.4 - 0.4 = 12.0. We can set up the equation (12.4x + 26) / (x + 5) = 12.0. Solving this equation, we find x = 85, which means the man took 85 wickets before his last match.

Explanation
Kanchan's average marks in 7 subjects is 75, which means the total marks he scored in these 7 subjects is 7 * 75 = 525.
His average in 6 subjects excluding Science is 72, which means the total marks he scored in these 6 subjects is 6 * 72 = 432.
To find the marks he got in Science, we subtract the total marks of 6 subjects from the total marks of 7 subjects: 525 - 432 = 93. Therefore, he got 93 marks in Science.

Explanation
The average number of visitors per day in a month can be calculated by taking the total number of visitors in the month and dividing it by the number of days in the month. In this case, the library has an average of 510 visitors on Sundays and 240 on other days. Since there are 4 Sundays in a month, the total number of visitors on Sundays in a month would be 510 * 4 = 2040. The total number of visitors on other days in a month would be 240 * 26 = 6240. Adding these two totals together gives us 2040 + 6240 = 8280. Dividing this by the number of days in the month (30) gives us an average of 8280 / 30 = 276. Therefore, the correct answer is 276.