Explanation

6(A's Capital) = 8(B's Capital) = 10(C's Capital)

We can write this as:

A's Capital = x

B's Capital = x × (6/8) = 0.75x

C's Capital = x × (6/10) = 0.6x

Now, we can write the ratio of their capitals as:

A's Capital : B's Capital : C's Capital = x : 0.75x : 0.6x

Divide each term by x:

A's Capital : B's Capital : C's Capital = 1 : 0.75 : 0.6

Multiply each term by 20 (the least common multiple of 1, 0.75, and 0.6) to eliminate decimals:

A's Capital : B's Capital : C's Capital = 20 : 15 : 12

So, the ratio of their capitals is:

20 : 15 : 12

Explanation

To divide Rs. 2000 in the ratio 3:2, we need to first calculate the total number of shares:

3 + 2 = 5

Then, we divide the total amount (Rs. 2000) by the total number of shares (5):

Rs. 2000 ÷ 5 = Rs. 400

Now, we multiply the share value (Rs. 400) by the respective ratio numbers to find the two shares:

Share 1 (3): 3 × Rs. 400 = Rs. 1200

Share 2 (2): 2 × Rs. 400 = Rs. 800

So, the two shares are Rs. 1200 and Rs. 800.

Explanation

To solve this proportion, we can use the following steps:

Write the proportion as a fraction: 3/x = 12/20

Cross-multiply: 3 × 20 = 12 × x

Simplify: 60 = 12x

Divide both sides by 12: x = 60/12

Simplify: x = 5

So, the value of x is 5.

Explanation

The total number of students in the school is 360 boys + 240 girls = 600 students.

The ratio of the number of boys to the total number of students is 360/600 = 3/5.

This can also be written as a fraction as 3:5 or as a decimal as 0.6.

Explanation

Ratio of oranges to peaches to strawberries = 2:3:4

If there are 8 oranges, we can set up an equation based on the ratio:

Number of oranges = 2x = 8

To find the value of x, divide both sides by 2:

x = 8 ÷ 2

x = 4

Now that we know x, we can find the number of peaches and strawberries:

Number of peaches = 3x = 3(4) = 12

Number of strawberries = 4x = 4(4) = 16

Total number of fruit items = Number of oranges + Number of peaches + Number of strawberries

= 8 + 12 + 16

= 36

So, there are 36 fruit items in the basket.

Explanation

Total amount =1000

Total parts of amount = 2+3 = 5

One part is + 1000/5 = 200

So Rabil amount part = 2 x 200 = 400

Explanation

Given:

The wages of 6 men for 15 days be Rs. 2100

Calculation:

As the wages of 6 men for 15 days be Rs. 2100

The wages of 1 man for 15 days = Rs. 2100/6 = Rs. 350

And, the wages of 1 man for 1 day = Rs.350/15

Now, the wages of 9 men for 12 days = (Rs.350/15) × 9 × 12 = Rs.2520

∴ The wages of 9 men for 12 days is Rs.2520.

Explanation

Given ratio: 35 : 84

Step 1: Find the GCD (Greatest Common Divisor) of 35 and 84  

GCD of 35 and 84 is 7

Step 2: Divide both terms by 7  

35 ÷ 7 = 5  

84 ÷ 7 = 12

Simplest form: 5 : 12

Explanation

She spent 4/9 of her money, which means she spent (4/9)x rupees.

She has 25 rupees left, which means she has (5/9)x rupees left (since 1 - 4/9 = 5/9).

We know that (5/9)x = 25, so we can solve for x:

x = 25 x (9/5)

x = 45

So, the girl had 45 rupees initially.

She spent (4/9) x 45 = 20 rupees.

The correct answer is: 20

Explanation

We can set up the proportion as:

6/m = 9/12

Cross-multiply:

6 × 12 = 9 × m

Simplify:

72 = 9m

Divide both sides by 9:

m = 72/9

m = 8

So, the correct answer is: 8