Mixture And Alligation Quiz! Math Trivia

Explanation
To find the ratio in which the grocer must mix the two varieties of pulses, we can set up a weighted average equation. Let the grocer mix x kg of the first variety and y kg of the second variety. The cost of the mixture will be (15x + 20y) / (x + y) = 16.5. Simplifying this equation, we get 15x + 20y = 16.5x + 16.5y. Rearranging the terms, we get 0.5x = 3.5y, which can be further simplified to x/y = 7/3. Therefore, the ratio in which the grocer must mix the two varieties of pulses is 7:3.

Explanation
To find the ratio in which the contents of the two casks should be mixed, we need to consider the ratios of wine and water in each cask.

In cask R, the ratio of wine to water is 6:7, while in cask S, the ratio of wine to water is 9:4.

To obtain a mixture with a ratio of wine to water as 8:5, we need to find a common ratio that can be applied to both casks.

By multiplying the ratio in cask R by 3 and the ratio in cask S by 2, we get the ratios of wine to water as 18:21 and 18:8 respectively.

Now, we can add the two ratios together to get a total of 36 units of wine and 29 units of water.

Therefore, the ratio in which the contents of the two casks should be mixed is 36:29, which can be simplified to 1:2.

Explanation
To find the amount of 100% concentrated acid needed, we can set up an equation using the concept of mixture. Let x be the amount of 100% concentrated acid to be added. The equation can be written as: 100x + 80(20) = 95(20 + x). Solving this equation, we get x = 60. Therefore, 60 liters of 100% concentrated acid needs to be added to 20 liters of 80% concentrated acid to get 95% concentrated acid.

Explanation
Let the original quantity of ghee be x kg.
Since 60% of the original quantity is pure ghee, 0.6x kg is pure ghee and 0.4x kg is Vanaspati ghee.
When 10 kg of pure ghee is added, the total quantity of pure ghee becomes 0.6x + 10 kg.
Since the strength of Vanaspati ghee becomes 20%, the total quantity of ghee becomes 0.6x + 10 + 0.2(0.4x) = x kg.
Simplifying the equation, we get 0.6x + 10 + 0.08x = x.
Solving the equation, we find x = 10.
Therefore, the original quantity of ghee was 10 kg.

Explanation
The milkman claims to sell the milk at cost price, but he actually gains 50% by mixing it with water. This means that for every 100 units of the mixture, 50 units are water and the remaining 50 units are milk. Therefore, the percentage of water in the mixture is 50%.

Explanation
To find out how much milk should be removed from the mixture, we need to calculate the current amount of milk in the mixture. The ratio of milk to water is 5:3, which means that out of every 8 parts of the mixture, 5 parts are milk and 3 parts are water. So, the current amount of milk in the 16-liter mixture is (5/8) * 16 = 10 liters.

To achieve a milk to water ratio of 4:3, we need to have 4 parts of milk for every 7 parts of the mixture. So, the desired amount of milk in the resulting mixture is (4/7) * (16-x), where x is the amount of milk to be removed.

Setting the current amount of milk equal to the desired amount of milk, we can solve the equation: 10 = (4/7) * (16-x).

Simplifying the equation, we get 70 = 64 - 4x.

Solving for x, we find that x = 2.

Therefore, 2 liters of milk should be removed from the mixture.

Explanation
Each time 4 liters of milk is taken out and replaced with water, the amount of milk in the container is reduced by 4/40 = 1/10. After 2 repetitions of this process, the amount of milk left in the container can be calculated as (1 - 1/10)^2 * 40 = (9/10)^2 * 40 = 81/100 * 40 = 729/25 liters.

Explanation
In each replacement, the amount of milk in the container decreases by 1/10th (4 liters out of 40 liters). After the first replacement, there will be 36 liters of milk left in the container. After the second replacement, there will be 32.4 liters of milk left. After the third replacement, there will be 29.16 liters of milk left. The total amount of liquid in the container after the third replacement is 40 liters (original amount) - 4 liters (first replacement) - 4 liters (second replacement) - 4 liters (third replacement) = 28 liters. Therefore, the ratio of milk to water in the final mixture is 29.16 liters of milk to 28 liters of water, which simplifies to 729/271.

Explanation
Let's assume that Priya bought x kg of the rice costing Rs 50 per kg and y kg of the rice costing Rs 60 per kg. The total cost of the rice mixture would be 50x + 60y.
She sold the mixture at Rs 67.2 per kg, making a profit of 20%. This means that the selling price was 120% of the cost price. Therefore, the selling price of the mixture would be 1.2(50x + 60y).
We can set up the equation: 1.2(50x + 60y) = 67.2(x + y)
Simplifying the equation, we get: 60x = 12y
Dividing both sides by 12, we get: 5x = y
So, the ratio of the two varieties of rice mixed is 2:3.

Explanation
To change the ratio of milk and water from 4:1 to 1:4, we need to add more water. The initial mixture contains 80 liters, with 4 parts milk and 1 part water. To make the ratio 1:4, we need 4 parts water for every 1 part milk. So, for every 5 parts of the mixture, 4 parts need to be water. Since the initial mixture contains 5 parts, we need to add 4 parts of water, which is 4/5 of 80 liters. This is equal to 64 liters. Therefore, the amount of water to be added further is 240 liters (80 + 64).

Explanation
The ratio of income for A and B is 3:2, which means that for every 3 units of income A has, B has 2 units. Similarly, the ratio of their expenditure is 5:3, meaning that for every 5 units of expenditure A has, B has 3 units.

Since both A and B save Rs.3000 at the end of the year, we can assume that their income is 5 units and their expenditure is 3 units.

Therefore, if 3 units of expenditure are equal to Rs.3000, then 1 unit of expenditure is equal to Rs.1000.

So, A's expenditure (5 units) would be 5 x Rs.1000 = Rs.5000.

Hence, the correct answer is 6000.

Explanation
When 12 more waiters are hired, the ratio of cooks to waiters changes from 6:26 to 3:16. This means that for every 3 cooks, there are 16 waiters. We can set up a proportion to solve for the number of cooks: 3/16 = x/28, where x represents the number of cooks. Cross multiplying, we get 3 * 28 = 16x, which simplifies to 84 = 16x. Dividing both sides by 16, we find that x = 5.25. Since the number of cooks must be a whole number, the closest option is 4. Therefore, there are 4 cooks.

Explanation
The servant worked for 60 days and received a total of Rs.480. Since he was paid Rs.10 for each day he worked, the total amount he earned from working is 60 x Rs.10 = Rs.600. This means that he was fined Rs.120 (Rs.600 - Rs.480) for being idle. Since the fine for each day of idleness is Rs.5, the number of days he was idle can be calculated as Rs.120 / Rs.5 = 24 days. Therefore, the servant was idle for 24 days.

Explanation
Since the monthly salaries of A, B, and C are in the ratio 5:4:9, let's assume their salaries as 5x, 4x, and 9x respectively. We are given that C's monthly salary is Rs.2000 more than A's salary, so we can write the equation 9x = 5x + 2000. Simplifying this equation, we get 4x = 2000, which means x = 500. Therefore, B's monthly salary is 4x = 4 * 500 = Rs.2000. To find B's annual salary, we multiply his monthly salary by 12, so B's annual salary will be 2000 * 12 = Rs.24000.