Explanation

Since the ratio of cats to dogs is 2:3, we can write:

Number of cats / Number of dogs = 2/3

We know there are 18 dogs, so:

Number of cats / 18 = 2/3

Cross-multiply:

Number of cats = (2/3) × 18

Simplify:

Number of cats = 2 × 6

Number of cats = 12

So, there are 12 cats.

Explanation

To find the amount of solution A and B:

Let the amount of solution A be 60 liters.

The ratio of A to B is 3:5.

Therefore, if A is 60 liters, then B is 5/3 × 60 =100 liters.

So, the solutions are 60 liters of A and 100 liters of B.

Explanation

Number of chocolate candies : Number of gummy candies = 3 : 2

We know that the total number of candies is 60, so we can set up the equation:

3x + 2x = 60

where x is a multiplier for both parts of the ratio.

Combine like terms:

5x = 60

Divide by 5:

x = 12

Now, multiply x by the ratio terms to find the number of gummy candies:

Number of gummy candies = 2x = 2(12) = 24

So, there are 24 gummy candies!

Explanation

Given that, P : Q = 8 : 15, Q : R = 3 : 2

P : Q : R = (8 x 3) : (15 x 3) : (15 x 2) = 24 : 45 : 30

∴ P : Q : R = 8 : 15 : 10

Here, consequent of first ratio should be equal to the antecedent of second ratio.

Explanation

6 persons working 8 hours a day earn Rs. 8400 per week.

First, let's calculate the total hours worked by 6 persons in a week:

6 persons x 8 hours/day x 7 days/week = 336 hours/week

Now, let's calculate the total amount earned per hour:

Rs. 8400 per week ÷ 336 hours/week = Rs. 25 per hour

Now, let's calculate the total hours worked by 9 persons in a week:

9 persons x 6 hours/day x 7 days/week = 378 hours/week

Finally, let's calculate the total amount earned by 9 persons in a week:

378 hours/week x Rs. 25 per hour = Rs. 9450 per week

So, the correct answer is: Rs. 9450

Explanation

1. 3/4 of the students do not know either Hindi or English.

This means that 1 - 3/4 = 1/4 of the students know either Hindi or English or both.

2. 1/6 of the students know English.

3. 1/8 of the students know Hindi.

Now, let's use the principle of inclusion-exclusion:

Number of students who know either Hindi or English or both = Number of students who know English + Number of students who know Hindi - Number of students who know both

We know that 1/4 of the students know either Hindi or English or both. We also know the number of students who know English (1/6) and the number of students who know Hindi (1/8).

Let x be the number of students who know both English and Hindi.

Then, we can set up the equation:

1/4 = 1/6 + 1/8 - x

Combine like terms:

1/4 = 7/24 - x

Add x to both sides:

x = 7/24 - 1/4

x = 7/24 - 6/24

x = 1/24

So, 1/24 of the students know both English and Hindi.

Explanation

1: The ratio of boys to girls is 4:5.

This means that for every 9 parts (4 parts boys + 5 parts girls), 4 parts are boys.

2: Calculate the total number of parts: 

 4+5=9 parts

3: Find the value of one part:

Total students=36

One part = 

36/9 = 4

4: Calculate the number of boys:

Number of boys=4×4=16 boys

Explanation

Let the two consecutive integers be x and x+1.

Their sum is given by: 

x+(x+1)=31

Simplify and solve for  

x: 2x+1=31

2x=30

Divide both sides by 2:

x=15

So, the two consecutive integers are:

15 and 15+1=16

Answer: 15 and 16

Explanation

To simplify the ratio of 12 to 18, divide both numbers by their greatest common divisor (GCD), which is 6:

12/ 6 = 2

18/ 6 = 3

Thus, the ratio of 12 to 18 in its simplest form is 2:3.

Explanation

To find the interest earned using the simple interest formula, use:

Simple Interest = 𝑃 × 𝑟 × 𝑡

where:

P is the principal amount ($1200),

r is the annual interest rate (5% or 0.05),

t is the time in years (2 years).

Substitute the values into the formula:

Simple Interest=1200×0.05×2

Calculate:

Simple Interest=1200×0.05=60

Simple Interest=60×2=120