SSC CGL Exam Tier-I: Quantitative Aptitude: Ratio And Proportion Quiz!

Explanation
Let's assume that the initial amount of liquid A in the can is 7x liters and the initial amount of liquid B is 5x liters. When 9 liters of the mixture is drawn off, the remaining amount of liquid A is (7x - (7/12)*9) liters and the remaining amount of liquid B is (5x - (5/12)*9) liters.

After the can is filled with liquid B, the ratio of A to B becomes 7:9. So we can set up the following equation:

(7x - (7/12)*9) / ((5x - (5/12)*9) + 9) = 7/9

Simplifying this equation, we get:

7x - (7/12)*9 = (5x - (5/12)*9) + 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 make the ratio 17:24 equal to 1:2, we need to find the difference between the two ratios. The difference between 17 and 1 is 16, and the difference between 24 and 2 is 22. Since we want to make the ratio smaller, we subtract the smaller difference from both terms of the ratio. Therefore, we subtract 16 from 17 and 22 from 24. This results in the ratio 1:2, which means that 10 is subtracted from each term of the original ratio.

Explanation
Let the weekly income of A be 9x and the weekly income of B be 7x. The weekly expenditure of A is (4/9) * 9x = 4x and the weekly expenditure of B is (3/7) * 7x = 3x. It is given that each saves Rs. 200 per week, so we can write the equation as 9x - 4x = 7x - 3x + 200. Simplifying this equation, we get 5x = 200, which implies x = 40. Therefore, the sum of their weekly incomes is 9x + 7x = 16x = 16 * 40 = Rs. 3200.

Explanation
After removing 3.8 L of the mixture, the amount of alcohol and water in the mixture remains the same. Since the ratio of alcohol to water in the original mixture was 5:3, the ratio will still be the same after replacing the removed mixture with water. Therefore, the ratio of alcohol to water in the resultant mixture is 5:3, which simplifies to 1:1.

Explanation
When Rama's income increases by 10%, his new income will be 110% of his original income. Since his expenditure increases by 12%, his new expenditure will be 112% of his original expenditure. As the ratio of his expenditure and savings remains the same, his new savings will be 110% divided by 112% of his original savings. Simplifying this, we get 0.9821, which is approximately 98.21%. Therefore, his savings increase by 7%.

Explanation
Let the three numbers be 3x, 4x, and 5x. According to the given information, we have 3x + 5x = 4x + 52. Solving this equation, we get x = 13. Therefore, the smallest number is 3x = 3 * 13 = 39.

Explanation
Let the present ages of Ram and Rahim be R and R+10 respectively. According to the given information, (R-10)/(R+10) = 1/3, which gives R = 20. Therefore, the present ages of Ram and Rahim are 20 and 30 respectively. Now, we need to find the ratio of their ages 5 years hence. After 5 years, Ram's age will be 25 and Rahim's age will be 35. The ratio of their ages will be 25/35 = 5/7. Simplifying this ratio, we get 3/5, which is the required answer.

Explanation
The ratio of milk to water in the third container is 3:2. This means that for every 3 units of milk, there are 2 units of water. In comparison, the other containers have higher ratios of milk to water. Therefore, the quantity of milk relative to water is minimum in the third container.

Explanation
When the initial mixture has a ratio of acid to water of 4:1, it means that there are 4 parts of acid and 1 part of water in the mixture. Therefore, the initial mixture contains 20 L of acid and 5 L of water. When 3 L of water is added to the mixture, the total amount of water becomes 5 L + 3 L = 8 L. The total volume of the mixture becomes 25 L + 3 L = 28 L. The ratio of acid to water in the new mixture is 20 L : 8 L, which simplifies to 5:2.

Explanation
Let the cost price of the second variety of tea be x. Since the price of the first variety is twice the second, the cost price of the first variety is 2x. The ratio of quantities of the first and second variety is given as 3:4, so let the quantity of the first variety be 3y and the quantity of the second variety be 4y.

The total cost price of the mixture is (2x * 3y) + (x * 4y) = 6xy + 4xy = 10xy.

The selling price of the mixture is Rs 36 per kilogram, so the profit made is 20% of the cost price. Therefore, the selling price is 120% of the cost price.

120% of the cost price = 36
1% of the cost price = 36/120
100% of the cost price = (36/120) * 100 = 30

So, the cost price of the mixture is Rs 30.

Since the cost price of the mixture is 10xy and is equal to Rs 30, we can solve for x and y.

10xy = 30
xy = 3

Substituting the value of xy in the cost prices of the varieties:
x = 3/y

The cost price of the first variety is 2x = 2(3/y) = 6/y
The cost price of the second variety is x = 3/y

Therefore, the cost prices of the two varieties of tea are Rs 6/y and Rs 3/y.

Substituting y = 1, we get the cost prices as Rs 6 and Rs 3.

Hence, the correct answer is Rs 21, 42.

Explanation
Let the cost of the first liquid be x per liter. Since the first liquid is costlier than the second by Rs 2 per liter, the cost of the second liquid would be (x - 2) per liter.

The ratio of the liquids is given as 3:5, so the cost of the mixture per liter would be (3x + 5(x-2))/8 = (8x - 10)/8.

The mixture is sold at Rs 120 with a profit of 20%, so the cost price of the mixture would be 120/1.2 = 100.

Setting the cost price of the mixture equal to the cost of the mixture per liter, we get (8x - 10)/8 = 100. Solving this equation, we find x = 101.25.

Therefore, the cost of the costlier liquid per liter is Rs 101.25.

Explanation
To find the proportion in which the two kinds of rice should be mixed, we can set up a weighted average equation. Let x represent the proportion of the cheaper rice (Rs 1.20 per kg) in the mixture. Then, the proportion of the more expensive rice (Rs 1.80 per kg) would be 1-x.

The cost of the mixture per kg can be calculated by taking the weighted average of the two rice prices:
(1.20x + 1.80(1-x)) = 1.75

Simplifying the equation, we get:
1.20x + 1.80 - 1.80x = 1.75
0.60x = 0.05
x = 0.05/0.60
x = 1/12

Therefore, the proportion in which the two kinds of rice should be mixed is 1 : 2.

Explanation
Let's assume the quantity of whisky in the jar is 100 units. Initially, the jar contains 40 units of alcohol. When a part of this whisky is replaced by another containing 19% alcohol, let's say x units of whisky are replaced. The remaining whisky in the jar is (100 - x) units. The total alcohol in the jar after replacement is 40 - 0.4x + 0.19x. Since the percentage of alcohol is 26, we can set up the equation (40 - 0.4x + 0.19x)/(100 - x) = 0.26. Solving this equation, we find x = 50 units. Therefore, 50 units of whisky are replaced.

Explanation
Every day, 80 L of wine is taken out of the container and an equal quantity of water is added. This means that the amount of wine in the container is decreasing by 80 L each day. After 4 days, a total of 320 L (80 L x 4) of wine has been taken out. Since the container initially had 240 L of wine, the remaining quantity of wine at the end of the fourth day is 240 L - 320 L = -80 L. However, it is not possible to have a negative quantity of wine, so the answer is 0 L. Therefore, the given answer of 47.40 L is incorrect.

Explanation
The tea trader mixed 20 kg of the tea costing Rs 3.50 per kg with 20 kg of the tea costing Rs 4 per kg. This resulted in a total of 40 kg of the mixture. The trader sold this mixture to the vendor at Rs 4.50 per kg, making a profit of 20%.

Explanation
The milkman delivers 10 L of milk to the first house and adds an equal quantity of water, making the total volume of liquid in the vessel 50 L. This means that after delivering to the first house, there are 40 L of milk and 10 L of water in the vessel. The same process is repeated at the second and third houses, so after delivering to the third house, there will be 40 L of milk and 10 L of water in the vessel. Therefore, the ratio of milk to water is 40:10, which simplifies to 4:1. This is equivalent to 61:64, so the correct answer is 61:64.

Explanation
Prabhu purchased 30 kg of rice at the rate of Rs 17.50 per kg, making a total cost of 30 * 17.50 = Rs 525. He mixed this with another 30 kg of rice and sold the entire quantity at the rate of Rs 18.60 per kg, making a total revenue of 60 * 18.60 = Rs 1116. Prabhu made a 20% overall profit, which means his total cost was 80% of the total revenue. Therefore, his total cost was 0.80 * 1116 = Rs 892.80. Since he already spent Rs 525 on the first 30 kg of rice, the cost of the second 30 kg of rice must be 892.80 - 525 = Rs 367.80. Thus, the price per kg for the second lot of rice is 367.80 / 30 = Rs 12.26. Rounding this to the nearest rupee, the answer is Rs 13.50.

Explanation
To make a profit of 50%, the selling price must be 150% of the cost price. Since the selling price is Rs 40 per liter, the cost price would be Rs (40/1.5) = Rs 26.67 per liter. The chemical costs Rs 50 per liter, so the cost of water per liter would be (50 - 26.67) = Rs 23.33. Therefore, the ratio of chemical to water should be 23.33 : 26.67, which simplifies to 7 : 8.

Explanation
Let's assume that the trader sells x kg of pulses at 8% profit and (50-x) kg of pulses at 18% profit.
According to the question, the trader gains 14% profit on the whole, so we can write the equation:
(x * 8/100) + ((50-x) * 18/100) = 14/100
By solving this equation, we find that x = 30 kg. Therefore, the quantity sold at 18% profit is 30 kg.