Answer: Option A. -> 12 : 19 : 26

Answer: Option D. -> Shristi

Answer: Option D. -> 6 :5
Given:

• The marks obtained by Vijay and Amit are in the ratio of 4:5
• The marks obtained by Amit and Abhishek are in the ratio of 3:2

To find:

• The marks obtained by Vijay and Abhishek in the ratio of x:y

Solution:Let the marks obtained by Vijay, Amit, and Abhishek be 4x, 5x, and 2y respectively.
According to the given information, the marks obtained by Amit and Abhishek are in the ratio of 3:2. Therefore, we can assume that Amit obtained 3k marks and Abhishek obtained 2k marks. Using this assumption, we can write the following equation:
5x/3k = 4/5Solving for k, we get k = 3x/4
Now, we can find the marks obtained by Amit and Abhishek as follows:Amit = 3k = 9x/4Abhishek = 2k = 3x/2
We need to find the ratio of marks obtained by Vijay and Abhishek, which is 4x:y. To find y, we can use the fact that the marks obtained by Amit and Abhishek are in the ratio of 3:2. Therefore, we can write:
9x/4 : 3x/2 = 3:2Solving for x, we get x = 8
Now, we can find the marks obtained by Vijay and Abhishek as follows:Vijay = 4x = 32Abhishek = 3x/2 = 12
Therefore, the ratio of marks obtained by Vijay and Abhishek is 32:12, which simplifies to 8:3 or 6:5 (dividing both sides by 4). Hence, the answer is option D, 6:5.
To summarize, the solution involves the following steps:

• Assume the marks obtained by Vijay, Amit, and Abhishek as 4x, 5x, and 2y respectively
• Use the given ratio between Amit and Abhishek to find a relationship between x and y
• Solve for x using the above relationship and the given ratio between Vijay and Amit
• Find the marks obtained by Amit and Abhishek using the assumed values of x and y
• Use the marks obtained by Vijay and Abhishek to find the required ratio.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option B. -> 18
Given,
Number of marks obtained by Sushil in English = 3x
Number of marks obtained by Sushil in Science = x
Number of marks obtained by Sushil in Mathematics = 5x
Total number of marks obtained by Sushil = 3x + x + 5x = 162

Therefore, 3x + x + 5x = 162
⇒ 9x = 162
⇒ x = 162/9
⇒ x = 18

Therefore, number of marks obtained by Sushil in Science = 18.

Hence, Option B (18) is the correct answer.

Answer: Option A. -> 9 :31

Answer: Option B. -> 7 : 5

Answer: Option C. -> 3 : 5
To solve this problem, we first need to find the amount of milk and water in the original mixture. If the ratio of milk to water in the mixture is 1 : 5, then for every 1 unit of milk, there are 5 units of water. If the mixture contains 24 litres, then:
Milk = 1 unitWater = 5 unitsTotal = 1 + 5 = 6 units
Milk in 24 litres of mixture = (1 unit ÷ 6 units) × 24 litres = 4 litresWater in 24 litres of mixture = (5 units ÷ 6 units) × 24 litres = 20 litres
Next, we need to find the amount of milk and water in the new mixture after 6 litres of the mixture are replaced by 6 litres of milk. The total amount of milk in the new mixture is 4 litres + 6 litres = 10 litres. The total amount of water in the new mixture is 20 litres - 6 litres = 14 litres.
Finally, we need to find the ratio of milk to water in the new mixture. The ratio can be calculated as follows:
Ratio of milk to water in new mixture = 10 litres ÷ 14 litres = 5 ÷ 7Reduced form of ratio = 5 ÷ 7 = 3 ÷ 5
Here is a summary of the key points in bullet form:

• The original mixture contained 24 litres of milk and water in the ratio of 1 : 5.
• Milk in 24 litres of mixture = 4 litres, and water in 24 litres of mixture = 20 litres.
• After 6 litres of the mixture are replaced by 6 litres of milk, the total amount of milk in the new mixture is 10 litres and the total amount of water in the new mixture is 14 litres.
• The ratio of milk to water in the new mixture is 3 : 5.

In conclusion, the correct answer is Option C, "3 : 5."

Answer: Option B. -> \(5\frac{1}{3}\)

Answer: Option B. -> 9

Answer: Option D. -> 9 ; 5

The ratio of speed of the dog to that of the hare is the ratio of distances covered by them in the same amount of time.

Let us assume that speed of the Hare is x units/sec

Then speed of the Dog = (3/5)x units/sec

Now, let us assume that the Hare takes n leaps in t seconds

Then, the Dog takes (3/5)n leaps in t seconds

Therefore, the ratio of the distance covered by the Hare to that of the Dog is

Distance covered by the Hare : Distance covered by the Dog

= (n * x * t) : ( (3/5) * n * (3/5)x *t )

= (n * x * t) : ( (9/25) * n * x *t )

= (25/9) : 1

Therefore, the ratio of the speed of the Hare to that of the Dog is

Speed of the Hare : Speed of the Dog

= (25/9) : 1

= 9 : 5

Therefore, the correct answer is Option D: 9:5

If you think the solution is wrong then please provide your own solution below in the comments section .