Explanation

Let's find the unknown value x using the proportion x : 5 :: 6 : 15.

We can set up the proportion as x/5 = 6/15.

Step 1: Cross-multiply

15x = 6 * 5

Step 2: Simplify

15x = 30

Step 3: Solve for x

x = 30 / 15

x = 2

Explanation

Given:

x : y = 3 : 4

y : z = 6 : 7

To combine, equalize y in both ratios (LCM of 4 and 6 is 12):

x : y = 9 : 12

y : z = 12 : 14

Combine to get: x : y : z = 9 : 12 : 14

Explanation

Given the calculation:

70 decreased in 2:5

New value = 70 * (2/5)

= 70 * 0.4

= 28

Explanation

To find the new quantity of cupcakes, let's calculate based on the given ratio of 7:6.

Initial quantity = 360 cupcakes

Ratio increase = 7:6

New quantity = 360 × (7/6) = 420 cupcakes

Explanation

Total amount = Rs. 5,376

Ratio = Ayesha : Sadia : Madiha = 8 : 7 : 6

Step-by-step:

Total parts = 8 + 7 + 6 = 21 parts

Sadia's share = (7 / 21) × 5376 = 1792

Explanation

Given Ahmed's income is Rs. 85,000 and expenditure is Rs. 51,000:

The ratio of income to expenditure is 85,000 : 51,000.

To simplify, divide both parts by their greatest common divisor, which is 17,000:

85,000 / 17,000 = 5

51,000 / 17,000 = 3

So, the ratio is 5:3.

Explanation

Given:

Asad : Sania = 2 : 3

Sania : Fahad = 4 : 3

To find the continued ratio, we need to make Sania's ratio equivalent in both. Let's adjust the ratios:

Asad : Sania = 2 : 3 = 8 : 12 (multiplied both parts by 4)

Sania : Fahad = 4 : 3 = 12 : 9 (multiplied both parts by 3)

Now, combining them:

Asad : Sania : Fahad = 8 : 12 : 9

Explanation

Ratio of boys to girls = 2:3

Number of boys = 12

Let's find the multiplier:

2x = 12

x = 6

Now, find the number of girls:

3x = 3 * 6

= 18

Explanation

Given proportion:

4 : 3 = 8 : p

First, let's find the relationship between 4 and 8:

8 = 2 * 4

Now, apply the same relationship to 3:

p = 2 * 3

p = 6

Explanation

To find the compound ratio, multiply the corresponding parts:

(3 * 8 * 25) : (4 * 15 * 28)

= 600 : 1680

Simplifying the ratio:

= 600 / 1680 = 5/14

= 5 : 14