Ratio

To solve the problem of determining how many litres of water should be added to change the milk to water ratio from 7:3 to 2:1, follow these steps:

1. Initial Composition: The total mixture is 80 litres. The ratio of milk to water is 7:3, which means the parts add up to 10 (7+3).

2. Calculate Initial Quantities:

• Milk in the mixture: litres.
• Water in the mixture: litres.

3. Desired Ratio: We want the ratio of milk to water to be 2:1.

4. Establishing Equation: Let x be the litres of water to be added. The new ratio condition is:

5. Solve the Equation: Cross-multiply to find x:

Thus, 4 litres of water should be added to make the ratio 2:1.

The correct answer is 4 litres.

To solve the problem, we need to find A + B : B + C : A + C given the ratios A : B = 5 : 6 and B : C = 6 : 7.

First, let's express A, B, and C in terms of a common variable to make calculations easy. Assume B = 6x. Then:

• Since A : B = 5 : 6, A = 5x.
• Since B : C = 6 : 7, C = 7x.

Now, calculate each part of the desired ratio:

• A + B = 5x + 6x = 11x
• B + C = 6x + 7x = 13x
• A + C = 5x + 7x = 12x

Therefore, the ratio A + B : B + C : A + C is:

• 11x : 13x : 12x

This can be simplified to:

• 11 : 13 : 12

The correct answer is 11 : 13 : 12.

To solve the problem, we need to find the cost price of the item given the marked price, discount, and profit percentage.

1. Understanding the Concepts:

- Marked Price (MP): The original price before discount.
- Discount: Reduction on marked price.
- Selling Price (SP): Price after discount.
- Profit Percentage: Percentage increase over cost price.
- Relationship:

2. Given Values:

- Marked price (MP) = Rs 500
- Discount = 20% → SP = 80% of MP
- Profit = 25%

3. Calculate Selling Price (SP):

4. Calculate Cost Price (CP):

Final Answer:

The cost price of the item is Rs 320.

To solve the problem, we need to find the age of B given the ratio of ages and their sum.

1. Understanding the Concepts:

- Ratio: The ages of A and B are in the ratio 3:5.
- Sum of Ages: The total of their ages is 40 years.
- We use the ratio to express ages in terms of a common variable.

2. Given Values:

- Ratio of ages = 3:5
- Sum of ages = 40 years

3. Calculate Ages:

Let the common multiplier be .
Then, A's age = , B's age = .
Sum:

4. Find B's Age:

Final Answer:

The age of B is 25 years.

To solve the problem, we need to find how many students play neither football nor cricket using the principle of inclusion-exclusion.

1. Understanding the Concepts:

- Total students = 50
- Students playing football (F) = 30
- Students playing cricket (C) = 25
- Students playing both (F ∩ C) = 10
- Students playing football or cricket or both (F ∪ C) = F + C - (F ∩ C)

2. Calculate Students Playing Football or Cricket:

3. Calculate Students Playing Neither:

Final Answer:

The number of students who play neither football nor cricket is 5.