Explanation

Initially, the salaries are in the ratio 1:3:4. Let's assume the salaries are x, 3x, and 4x.

After the increases:

A's salary increases by 5%, so the new salary is x + 5% of x = x + 0.05x = 1.05x

B's salary increases by 10%, so the new salary is 3x + 10% of 3x = 3x + 0.10(3x) = 3.30x

C's salary increases by 15%, so the new salary is 4x + 15% of 4x = 4x + 0.15(4x) = 4.60x

Now, let's find the ratio of the increased salaries:

1.05x : 3.30x : 4.60x

To simplify, divide each term by 0.05x (the smallest common multiple):

1.05x / 0.05x = 21

3.30x / 0.05x = 66

4.60x / 0.05x = 92

So, the increased salaries are in the ratio 21:66:92.

Explanation

9/162=x/306

X=9/162 × 306

X= 17

Explanation

For distribution between A & B the proportion has to be 2:3

Thus when A gets 2 units, B gets 3 units

So A gets ₹20/- & B gets ₹30/-

Distribution between B & C has to be 2:3

If ₹30 is 2, then 3 has to be ₹45/-

So ₹ 95,000/- to be divided between A, B & C shall have to be in the proportion of

20:30:45

Thus A gets ₹20′000/- B gets₹30′000/- and C gets ₹45000/-

Explanation

12 men=15women

1man=(15/12)=(5/4) women

7 men=35/4 women

(35/4+5 )=55/4

15 women=14 days

55/4 women=(15*14*4)/55= 168/11 days

Explanation

To find the ratio of 12 minutes to 1 hour, we first convert 1 hour into minutes:

1 hour = 60 minutes.

Now, the ratio of 12 minutes to 60 minutes is:

12​/ 60= 1/ 5​

Explanation

To find the amount of sugar needed for 1 cup of flour, we set up a proportion based on the given ratio:

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.