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

Explanation

He spent 3/5 of his savings, which means he spent (3/5)x.

He was left with Rs. 2,000, which means his initial savings minus the amount he spent equals Rs. 2,000:

x - (3/5)x = 2,000

Simplifying the equation:

(2/5)x = 2,000

Multiplying both sides by 5/2:

x = 2,000 x 5/2

x = 5,000

So, the man's initial savings were Rs. 5,000.

The correct answer is: Rs. 5,000

Explanation

Let N of 1/12 = 3/48.

Then, N = 3/48 x 12 = 3/4

Explanation

Let third number = x

First number = 120/100 x = 6x/5

Second number = 150/ 100x = 3x/2

Ratio of two numbers = 6x/5 : 3x/2 = 12x : 15x = 4:5

Explanation

To find the fourth proportional, we need to set up a proportion:

60 : 48 :: 30 : x

Where x is the fourth proportional.

We can rewrite this as: 60/48 = 30/x

Cross-multiplying, we get: 60x = 30 × 48

Simplifying, we get: 60x = 1440

Dividing both sides by 60, we get: x = 24

So, the fourth proportional is 24.